A three-dimensional (3D) parabolic equation acoustical propagation code has been developed and run successfully. The code is written in the MATLAB language and runs in the MATLAB environment. The code has been implemented in two versions, applied to: (1) Horizontal low-frequency (100 to 500 Hz) propagation through the shallow water waveguide environment; (2) Vertical high-frequency propagation (6 to 15 kHz) to study normal-incidence reflection from the lower side of the ocean surface. The first edition of the code reported on here does not implement refinements that are often found in 2D propagation models, such as allowing density to vary, optimally smoothing sound-speed discontinuities at the water/seabed interface, and allowing an omni-directional source. The code is part of a development effort to test the applicability of 2D (and N by 2D) models, which have more refinements than this model, to the study of fully 3D propagation problems, such as sound transiting steep nonlinear coastal-area internal waves and/or sloping terrain, and to provide a numerical tool when the full 3D solution is needed.