Suspense starts to build in this story as we wonder where the family is, and when they are going to appear, if at all. The first infusion of suspense is after the breakfast food that is prepared so fastidiously by the machines is not eaten. All of that food is thrown away, after sitting there for quite some time. At this point, the reader has to wonder to oneself, where is the family? Why didn't they eat the breakfast? From then on, any noticable absence of the family members builds on that initial suspense; the garage opens but no car leaves. Reminders are given, but echo down empty hallways. All of this builds and builds until we are taken outside, and the imprints of people are described on the blackened wall of the house. Then, we realize that the family, mid-play, was completely decimated, as was much of their city.
After we realize what happened to the family, the suspense lessens a bit; we already know that they died, now we are just hanging in there for the ride, to see how Bradbury is going to end the story. Our suspense flares up again as the poor, sick dog comes in the house. We rally around it, hoping it will survive, and are sorely disappointed and depressed when it doesn't. Another flare of suspense occurs when the house freaks out and sets itself on fire--this is an interesting development, and we wonder if it will really burn itself down.
The suspense in "There Will Come Soft Rains" is mainly evident as the audience realizes that the family is not there, and that something is awfully wrong as a result of it. The absence of human life in a world that is filled with technology is a strange and discomfiting one indeed, and that is why it is so suspenseful. I hope that helped; good luck!