The development of a special‐purpose microcomputer system (calledPESOGEN= parabolic equation solution generator) that performs high‐speed PE model computations using the split‐step Fourier algorithm was reported previously [L. Nghiem‐Phu, S. C. Daubin, and F. Tappert, J. Acoust. Soc. Am. Suppl. 175,S26 (1984)]. Applications ofPESOGENto three‐variable modeling are reported here. (1) Full‐wave computations of pulse propagation, signal waveforms, and cross‐correlation functions requirep(r,z,t), a function of three variables.PESOGENcomputesp(r,z,ω) in the frequency domain for many values of ω sequentially, and then obtainsp(r,z,t) in the time domain by numerical Fourier transforms [L. Nghiem‐Phu and F. Tappert, J. Acoust. Soc. Am. Suppl. 168,S51 (1980)]. Examples of pulse transmission to long range in deep and shallow range‐dependent oceans are presented, with emphasis on numerical accuracy (tested by time‐domain reciprocity) andPESOGENthroughout times (typically less than 1 h). (2) Full‐wave computations of responses of directional receivers to line‐radiation sources requirep(x,y,z), a function of three variables. Using specified farfield beam patterns,PESOGENcomputesp(x,φ,z] for many values of the azimuthal angle φ sequentially, and then obtains TL′ = TL − ASG, where ASG is the array signal gain [F. Tappert and L. Nghiem‐Phy, J. Acoust. Soc. Am. Suppl. 175,S63 (1984)]. Examples of directional receiver response to long range sources in three dimensions are presented, with emphasis on full‐wave effects in the beam deviation loss andPESOGENthroughput times. Conceptual designs of large special‐purpose computer systems for three‐variable propagation modeling using multiplePESOGENunits in parallel with single‐instruction multiple‐data architectures are also presented.