Theoretical research was mainly focused on single-acting liquid ring pump with circular case and the traditional formula has great deviation from the practice for aviation liquid ring pump with small volume. In this study, theoretical formula of liquid ring pump was revised based on the variable process of residual gas in the actual operating cycle. Then the compression ratio of single-acting or double-acting liquid ring pumps with circular or elliptic cases was solved respectively, the compression ratio characteristic curves of different pump structures were obtained and the inner boundary of liquid ring was drawn in polar coordinates. Finally, the gas–liquid interface in the pump was accurately captured by the gas–liquid two-phase numerical simulation, and the flow field characteristics and performance differences of liquid ring pumps with different pump cases were analyzed. Results showed that double-acting liquid ring pump has a large suction capacity and the pump with elliptic case has faster compression speed and better power-to-weight ratio than that with circular case.