A classical mechanical generalized Langevin formalism is applied to the study of gas-surface collisions. Procedures are described for constructing generalized friction and fluctuating forces which accurately represent the motion of real solids, and which can be conveniently implemented in a classical stochastic trajectory calculation. Energy transfer computed using this approach for He-W collisions is in excellent agreement with results of a quantum mechanical distorted wave calculation employing the same phonon density of states. The method is further applied to the study of residence times and sticking probabilities. Results indicate that the stochastic trajectory approach is feasible and capable of accurate simulation of gas-surface collision phenomena.