The present study describes a method for the prediction of steady, transonic, two–dimensional fluid flow in planar nozzles. The present work is essentially an extension of earlier work by Parameswaran  to two dimensions. The steady Euler equations are expressed on a nonorthogonal grid system formed by streamlines and lines parallel to the y axis. Grid–based velocity components are employed to represent the velocity field of the flow. The differential equations are discretized in a finite–volume fashion. A partially staggered grid system is employed to store the variables. The upwind differencing scheme is employed to approximate the convective terms. A modified version of the SIMPLE algorithm is employed to solve the coupled, nonlinear equations. For flows with shocks, a novel procedure is employed to capture the shock within a cell on each stream tube.