What is the setting of "A Sound of Thunder" by Ray Bradbury?

The basic setting in which the story takes place is a jungle in which a safari is being conducted.  The characters are on a type of safari- like hunt for a Tyrannosaurus Rex.  The safari is taking place during the prehistoric times, courtesy of a time machine in which people from the future can pay a sum of money and travel back in time.  It is this setting in the past with people from the future in which Bradbury is able to construct his story, establishing the setting for it.  The characters may be of the future, traveling back in time to the prehistoric past, but Bradbury does not let this obscure the basic flaws of what it means to be human.  This character trait is something that we see in our own sensibilities in the current setting and is reflected in these characters from the future who have traveled back in time.  This helps to bring out what Bradbury would see as an intrinsic human characteristic that is able to be evoked for all human beings regardless of time period.  In this, the characters from the future who are immersed in a setting of the past display the same type of human qualities that define what it means to be human throughout time.

Because "A Sound of Thunder" is an exploration and critique of the hubris of using advanced technology for frivolous purposes, the story has two settings: the age of dinosaurs and the "present day" in the United States in a near future shortly after a presidential election.

Eckels, the main character, has paid a large sum of money to travel back on a "safari" to kill a Tyrannosaurus rex. The present day of the story, as we encounter it through Eckels, is bureaucratic and technological, dominated by his experience at the time machine company. He and the man booking his safari are both grateful that Keith, rather than Deutscher, a potential dictator, won the recent election.

Bradbury spends more time on the dinosaur age, describing some of what Eckels sees as follows:

The jungle was high and the jungle was broad and the jungle was the entire world forever and forever. Sounds like music and sounds like flying tents filled the sky, and those were pterodactyls soaring with cavernous gray wings

Most of Bradbury's descriptive energy, however, is spent on describing the fearsome Tyrannosaurus rex—so much bigger than any animal in the present-day world—and the theoretical wonders and dangers of time travel.

Eckels and his party return from the safari, Eckels having caused problems by panicking and killing a prehistoric butterfly. Now, changes in the setting reveal that he has, in fact, changed history. He is first alerted to the change by spelling variations on the safari sign, then discovers that in this new version of the present, Deutscher has become president.

"A Sound of Thunder" takes place in three distinct settings. When the story begins, the action is occurring in the office of Time Safari, Inc., at the present time, after a very significant presidential election in which the democratic leader defeated the candidate that would have led to tyranny. 

The setting then changes to the past when dinosaurs roamed the earth. The men are on a safari to hunt the T Rex.  Time Safari Inc has established rules and procedures to control their impact on this environment, but ultimately they are unable to maintain complete control. This setting is significant because it represents man's interference in natural events and our desire to control natural processes.  

The setting then changes back to the original time and location, but with an alternative reality due to the effect of the interference in the past.  Now instead of the democratic leader winning the presidential election, the fascist leader has won. This small change in the setting changes every aspect of daily life for the characters in the story. This setting is significant because it represents the importance of man's responsibility for his actions.

In literature, the setting provides the reader with enough information to allow him or her to visualize essential elements of any story and is particularly relevant in a story in which the theme revolves around events which have the potential to change the future. Such is the situation in Ray Bradbury's A Sound of Thunder , where the so-called, Butterfly effect, which Eckels brings effect to, has far-reaching implications. In this case, the setting includes the future and the past and time, therefore, is an integral part of setting. 

Basically, the setting includes, as a reader would expect, the surroundings or location but also includes the historical aspect, which gives the story its depth and context. Setting also allows for character development and, in this case, we see how Eckels failure to respect his environment, having traveled back from the year 2055, can have disastrous implications: 

"Its purpose is to keep you from touching this world of the Past in any way. Stay on the Path. Don’t go off it....For any reason!"

Transported back in time, Eckels carelessly steps on a butterfly, despite being reminded not to step off the path in an environment he has been privileged to experience through the benefits of time travel. The benefits of technology are also relevant to the setting as, without technology, the "anti-gravity metal" would not be able to protect the environment. It seems however, that even technology could not protect this world as human nature revealed its flaw. Eckels actions and even the outcome of the story are thus influenced by the setting. The importance of the setting of A Sound of Thunder can be summed up: 

“messing around in Time can make a big roar or a little rustle in history.”

“A Sound of Thunder” is science fiction story set in the future.  It takes place in the year 2055, and they travel back in time to the time of the dinosaurs.

The story opens at Time Safari, Inc.  It is a time travel company.  They have this sign.

TIME SAFARI, INC.
SAFARIS TO ANY YEAR IN THE PAST.
YOU NAME THE ANIMAL.
WE TAKE YOU THERE.
YOU SHOOT IT.

The company takes people back to any year they want to hunt any animal they want.  They go to the time of the dinosaurs, where a man named Eckels wants to shoot.  He is told to stay on the path, because if they leave the path there could be disastrous consequences.

Eckels does accidentally step off the path onto a butterfly.  Then he changes the future.  When they return to 2055, there is a new president and things are spelled differently.

This story is an exploration of the law of unintended consequences.  If you make one small action, it can have a ripple effect—the butterfly effect.

The story actually has two or three settings, depending on how you view them. In its framework, the action is set in the future, presumably in the year 2055. Time travel is possible, but only by following strict requirements. The business called Time Safari, Inc. takes people back in time to shoot and kill exotic, now-extinct animals. The story begins and ends in this office.

The main plot involves a hunting party that uses the time machine to go back to prehistoric days. Their goal is to kill a Tyrannosaurus rex that would otherwise be killed by a falling tree. This setting is obviously vastly different, almost primeval. It’s a tangled green jungle, outfitted with a Path that the hunters must stay on in order to not disturb or injure anything. The dinosaur appears and is killed, the tree falls, and the hunters return to their own time.

But is it their own time? Immediately they notice changes because one of the party members had stepped off the Path. They return to the Time Safari, Inc. office, but things are now slightly different – enough, that it could be considered a third setting. This leads to the point of the story: time travel has the ability and danger of changing the future. 

What is the importance of the setting in "A Sound of Thunder"?

Setting is of great importance in "A Sound of Thunder" both because of the direct danger the setting poses to the characters, and to the ability of the setting to affect the flow of history.

The characters are engaged in a time safari - using a time machine to travel to the distant past in order to hunt animals that are extinct in the modern era. In this particular case, they are hunting a tyrannosaur, so their trip, and its setting, necessarily preclude any possibility of assistance. If anything goes wrong or anyone is injured or killed, their only option is to retreat to the machine and return to their own time.

Furthermore, the setting is important because influencing it in any way may have unforeseen effects upon the way that history plays out, as the characters know it. This means that any change or interaction with the setting, no matter how small, might alter the way life on Earth plays out; they could inadvertently cause the extinction of humanity through some innocuous action. This is demonstrated at the end of the story, when Eckels accidentally kills a butterfly, resulting in the world that they return to being different from the one they left.