Numerical methods based on Wiener Chaos expansions are effective methods for solving stochastic partial differential equations driven by Brownian motion. These methods allow for the separation of random and deterministic effects in a rigorous manner by discretizing the stochastic partial differential equation into a system of deterministic equations for the coefficients of the Wiener Chaos expansion. In this presentation, we describe the application of a numerical method based on Wiener Chaos expansions to the solution of some stochastic evolution equations and compare our results with the exact solutions of the equations.