A new method for the numerical simulation of the stochastic electromagnetic environment of a mode-stirred chamber is presented in this paper. This method is based on the plane-wave integral representation for the fields and uses a Monte Carlo simulation to replace the analytical integration by numerical summation. Therefore, a field generator is implemented as a program. The numerically generated field distributions and spatial correlation functions are compared to the analytical solutions for the validation of the field generator. With this generator, the field coupling to a simple transmission-line structure can be numerically simulated. The coupled current or voltage has to be regarded as a stochastic value as well, and therefore, parameters like the mean value and the standard deviation along the line are calculated. For the special case of a matched line, an analytic solution is introduced in order to validate the numerical results. The simulation also allows for investigating the statistical distribution and correlation of the coupled current along the transmission line. Numerous simulated results are compared with measurements.