The paper illustrates a computer modelling method for the generation of a highly correlated pseudorandom process with a desired power density spectrum. The samples of the pseudorandom process are generated as the output of a cascade connection of a correlation shaping transversal filter and a reconstruction filter with statistically independent samples fed to the input. Such a generation method needs a much smaller number of mathematical operations compared with the traditional transversal filtering method, and does not require any special or careful filter design for each process parameter, as is necessary in the application of an IIR filter.