A method of solution of the shallow water equations in their primitive form that yield solutions free of numerical oscillations, is presented. The method is based on the least squares collocation concept. The focus is on the accuracy of the solution procedure. Comparison of the numerical solution with analytic solutions for problems of irregular geometry are presented. Key features are the ability of the method to solve the equations in an irregular domain with a completely orthogonal computational mesh and the inherent nondissipative noise control of the temporal and spatial approximations. ¿ American Geophysical Union 1993