A Monte Carlo technique is described for finding the response of a horizontally stratified cold plasma to a plane impulsive wave at vertical incidence. The effects of electron collisions with neutral particles and a vertical magnetic field are included in the analysis. The technique is arrived at by replacing a continuous scattering process (by continuous we mean the electrons are uniformly distributed through any horizontal plane in the plasma ( with a sequence of scatters. All orders of scatter are computed from this sequence of scatters, and the Monte Carlo approximation to the exact solution is the sum over these orders of scatter. The method is applicable for any electron density function N(z), collision frequency, or cyclotron frequency. The Monte Carlo solution presented here is valid only for small and intermediate values of time; the solution diverges for large values of time. The Monte Carlo method is applied to the uniform half-space problem since there are exact and approximate analytical solutions to compare with the Monte Carlo results.