It was used to destroy the German HQ in Moscow after the Seargent commanded the group to blow up the remaining enemies hiding in the second floor on the mission Demolition. In this mission, you make your way to the German stronghold and eliminate all the enemies on the first floor, the other Germans barricade themselves inside the second floor. Then, you place the TNT on various points on the building. When you finish, run, and watch the explosion.
Dynamite appears in Shangri-La during the Time Travel Will Tell Easter egg. During the eleventh step, the player must pick up a bag of Dynamite. After completing the next step, the player must use the Dynamite to destroy the wall that appears in front of the Pack-a-Punch Machine. The players will go back to the present however before the wall is destroyed. The wall will be gone though, allowing the focusing stone to be picked-up.