The classical depth averaged St. Venant equations for shallow free surface flow are extended to treat problems with nonhydroslatic pressure and nonuniform velocity distributions. The equations required to solve for the additional degrees of freedom are derived by a moment weighted residual method from the fundamental Reynolds equations. The new equations are derived in detail in one horizontal dimension and evaluated for the basic problems of uniform flow and small amplitude waves. With further study and application, these new equations may offer a means for obtaining greater detail over a wider range of problems than is presently practical.