This report presents the mathematical formulation and verification of a numerical model that simulates wave transformation and longshore current over a bar and trough beach profile. The model is intended for application on projects involving dredged material berms and other situations where a bar and trough topography prevents use of simple analytic or numerical solutions that are restricted to a uniformly sloping beach. The model is called NMLONG, an acronym that stands for Numerical Model of the Longshore current, and it can be conveniently run on a desk-top (personal) computer. The model incorporates all known features of the wave and longshore current system that appear in research-type engineering models run on mainframe computer systems. These features include wave and wind driving, wave breaking and reformation over multiple bar and trough profiles, and lateral mixing. The model also allows choice of linear or quadratic bottom friction and regular or random wave heights as options. The main restriction of the model is longshore uniformity of the waves and beach topography. The model was verified with several field and laboratory data sets. The wave calculation reproduced cross-shore heights of laboratory monochromatic waves on both plane-sloping and bar and trough profiles, and it also reproduced field measurements of wave height frequency of occurrence at different depths in the surf zone. The longshore current model reproduced measured currents on plane-sloping laboratory beaches and currents measured in the field or irregular bottoms. Sensitivity analyses examined linear and nonlinear bottom friction formulations, strength of lateral mixing, effect of wind on setup/setdown and the current, and wave-current interaction.