A two-dimensional, compressible, finite volume, magnetohydrodynamic (MHD) solver for simulating inviscid and fully ionized plasma flow is developed to compute the flow field in Magnetoplasmadynamic (MPD) thrusters. Unsteady Euler's equations with body forces and Joule heating as momentum and energy sources are solved along with the solution of unsteady magnetic flux density equation derived from Maxwell's equation. The flow solver is validated against some benchmark gas dynamic problems. The MHD part of the solver is validated by computing a flared anode 2D MPD thruster flow. The effect of geometric configuration on the thruster performance is a studied by varying the length of cathode in a straight anode MPD thruster. A study on the effect of inlet mass flow rate is also performed for short (13 mm) and long (41 mm) cathode cases. The results are analyzed to understand the flow physics and to identify the configuration that yields better performance characteristics.