A four-cylinder pneumatic motor is proposed and analyzed as an expansion machine to be used in a compressed-air energy storage system. The motor uses a combination of displacement work at constant pressure followed by a sequence of expansion of the air. The four double-acting linear cylinders form two groups of chambers, each with one chamber for the constant pressure displacement work and three chambers in which the air is expanded. The operation of the system and especially the allocation of the functions were analyzed, and the system was simulated with the produced forces given by the cylinders to the torque generated from the crankshaft. A demonstration set-up was also realized with a specific motivation which was to show how demonstration objects could be realized with very limited infrastructure. Finally, the motor energetic efficiency was calculated.