The magnetoplasmadynamic (MPD) accelerator is a device capable of accelerating a plasma-gas stream to a very high velocity using interacting electric and magnetic fields. The analysis and descriptions of the internal processes and acceleration schemes within the MPD accelerator have been investigated by many researchers, but usually the mathematical models were greatly simplified on either a fluid-dynamical or electromagnetic approach. This treatise combines classical gasdynamic and electromagnetic descriptions of the MPD process, based on fundamental laws of mass conservation, momentum conservation, and energy conservation considerations. Our axisymmetric mathematical model requires the solution of complete magnetohydrodynamic differential equations. The gas flow has been assumed to be nonviscous, and the net free charge density at the anode and cathode boundaries has been set to zero. Twelve differential equations describe the MPD arc model and were solved for twelve unknowns. Using a finite-difference technique, the equations are put into a form that is adaptable for computer solution. Boundary conditions, an I,J cell matrix, and a cylindrical coordinate axis are defined, and the equations are computer-solved in an iterative manner. After four iterations, however, physically large and unrealizable variable values occur, and the trend indicates a divergent rather than a convergent solution. Examination of the computational results have shown that solutional instability exists in this case. When dealing with numerical solutions concerned with supersonic flow, solutions may show instabilities. It appears in the case of this study that a numerical scheme has to be developed which will check these instabilities in some manner. A study of other numerical methods is therefore recommended at this point. Perhaps a more suitable method can be applied in a manner which will afford a better and more meaningful solution to this problem.