What were the military objectives of the Vietnam War?
Neither side really had objectives that were mainly military in this war. Both sides essentially knew that a complete military victory would not be possible.
For the United States, the main military objective was to kill as many of the enemy as possible. The US was fighting on an ally’s territory, so it was not as if the US was trying to conquer a certain geographic area. Instead, it wanted to kill enough of the enemy to make the enemy give up.
For the Vietcong and the North Vietnamese, it was clear that they could not defeat the United States militarily. They could never drive the US out of South Vietnam if it wanted to stay. So their objective was to wear down the US to the point where it no longer wanted to stay. The communist forces wanted inflict losses on the US, of course. But their main goal was simply to keep fighting until the will of the US was sapped and it gave up the fight.