A three-dimensional explicit time marching algorithm has been developed for the numerical solution of inviscid internal flows. The formulation uses the natural streamline co-ordinate system. The unsteady Euler equations in non-conservative form are expressed in terms of the extended Riemann variables and the flow angles. Along the characteristic trajectories in the space-time domain, these equations reduce to a system of ordinary differential equations. Boundary conditions are also implemented in characteristic form. Shock waves are calculated after performing a one-point shock correction that maintains conservation across the discontinuity.