The objective of this thesis is to explore how human beings manipulate their dexterous operation skills to produce follow shot, stop shot, and draw shot while playing billiard. According to basic mechanics, the forces exerted on a billiard ball are analyzed in three different conditions. They include the cue stick hitting the cue ball, collision between the cue ball and the object ball, and the interaction between the ball and the surface. Mathematical models for those three fundamental techniques: the follow shot, the stop shot, and the draw shot, are developed by incorporating the rolling resistance. The friction between the surface and the ball, and the dent on the surface due to the mass of the ball are considered. Furthermore, reverse derivations are also implemented to solve initial hitting conditions between the cue stick and the cue ball for certain final states for the cue ball and the object ball. Computer simulations in virtual reality are conducted using the 3D Studio Max 8 software tool. Opinions from billiard experts are also collected for the purpose of verification. Based on simulation results, reversed derivation can accurately predict final states of the cue ball and the object ball for both stop shot and draw shot. However, for the case of follow shots, final position of the object ball cannot be fully determined. Besides, no unique solution exists for the hitting condition in all three types of shot.