The governing equations for flow of an incompressible and cohesionless material are solved approximately by a new procedure. In this procedure the equilibrium equations and the yield criterion are satisfied identically through invocation of the Airy stress function and the Sokolovski functions. The problem analysed pertains to radial flow in a wedge-shaped hopper for which some experimental results are available. The computed results exhibit qualitative features which are similar to those obtained by other investigators using different solution procedures. Quantitatively however the present results are in better agreement with experimental results, than theoretical results obtained hitherto subject to similar assumptions.