Numerical modeling of Magneto-Plasmadynamic (MPD) thrusters is initiated using the recently developed three-dimensional version of the MACH code. The new version has undergone a series of verification cases to confirm mass and energy conservation and accurate computation of magnetic field diffusion. These cases also allowed analysis of grid sensitivity in the azimuthal direction. The MPD modeling addresses complete coaxial thruster geometries including extended computations to include the plume region in order to fully capture the flowfield. Steady state computations using helium propellant at 0.5g/s and current levels of 7kA, 8kA and 9kA show expected trends for thrust and voltage. Comparisons of the magnitude to the established analytic thrust relationship and to predictions of the 2-D axisymmetric version of the code show discrepancies that require further interpretation. The computational resources required to complete steady state simulations of such advanced geometries are quite taxing, so the code has been parallelized for execution using multiple supercomputer CPUs.