The barotropic mode of the Primitive Equations is considered. Thecorresponding equations resemble the Euler equations of incompressible flows with marked differences. The existence and uniqueness of solutions for the linearized equations is proven; the proof is based on the study of a nonstandard boundary value problem. In the nonlinear case, sev- eral schemes inspired by the projection method are proposed and their stability is studied. Finally, numerical simulations are described using one of these schemes, closely related to the pressure correction projection scheme.