A semi-analytical model of the Panama throughflow is presented. The model expresses the throughflow transport as a function of deep water formation in the North Pacific and in the North Atlantic, and of the Panama Gateway depth. The model is derived from the integral of the momentum equation along a circumpolar path, and can be interpreted from the point of view of the vorticity balance. The important conditions are whether the deep water, whose location is considered to be above the bottom water formed around Antarctica, originates from the North Atlantic or from the North Pacific, and whether the Panama Gateway is shallower than the lower boundary of the deep water. The present model indicates that the barotropic transport through the Panama Gateway is eastward, except for the case where the deep water is formed in the North Pacific and the sill of the Panama Gateway is shallow. The baroclinic structure of the Panama throughflow depends on whether the deep water is formed in the North Pacific or in the North Atlantic. These qualitative implications of the model are consistent with recent numerical studies and proxy-based paleoceanographic studies. Numerical experiments performed in the present study reinforce confidence in the semi-analytical model.