This work continues a series of papers where we propose an algorithm for quasioptical modeling of electromagnetic beams with and without mode conversion. The general theory was reported in the first paper of this series, where a parabolic partial differential equation was derived for the field envelope that may contain one or multiple modes with close group velocities. Here, we present a corresponding code PARADE (PAraxial RAy DEscription) and its test applications to single-mode beams in vacuum and also in inhomogeneous magnetized plasma. The numerical results are compared, respectively, with analytic formulas from Gaussian-beam optics and also with cold-plasma ray tracing. Quasioptical simulations of mode-converting beams are reported in the next, third paper of this series.