A two-dimensional numerical model is presented for the study of the Chicago area lake breeze. The hydrostatic approximation used by previous workers in this field is not employed. Instead, the complete z-momentum equation is solved and the equation of continuity is retained in its original form. The numerical model employs a staggered mesh, and Alternating Direction Implicit methods are used for the integration of the equations. Computational stability is achieved without external filters, upstream space differencing, or artificial horizontal diffusion terms.