The acceleration of a plasma by a capacitor discharge between coaxial electrodes is studied for (1) a shock tube having an initially uniform gas distribution and for (2) a plasma gun which accelerates a constant mass into a vacuum. Differential equations written for the first case for a simple snowplow model and solved by analog computer, are found to closely predict peak plasma velocities for a certain range of pressures. However, experimental study by means of a ``difference'' magnetic probe shows that the actual current distribution in the space between the electrodes is rather complex. Near the time when peak plasma velocity is reached, the first pulse splits into two pulses and persisting loop currents form in the plasma. An efficient mode of plasma acceleration which produces faster and more sharply defined shock waves is observed at low pressures when the center electrode is initially positive. Computer solutions are also obtained for the plasma gun, which seems to be intrinsically capable of greater efficiency than the shock tube.