The Stirling refrigerator, as an important type of Stirling machine, is widely used in both civil area and space technology. However, many of the existing models of the Stirling refrigerator are compatible with one specific type, and there is usually a contradiction between reflecting the reality accurately and giving an analytical solution. Based on the thermoacoustic theory, it is assumed that the acoustic inertance, the acoustic compliance, the flow resistance in the regenerator and the thermodynamic process in the working spaces are the major factors that affect the overall performance of the Stirling refrigerator. Therefore, by adopting the transmission line model and the polytrophic process equation, this paper proposed a general model which is applicable to various types of Stirling refrigerators and is able to give analytical solutions that can reveal some basic principles. By comparison, the simplified cases of the general model is found to be equivalent to some of the existing models, and a good agreement is achieved among the general model, the experiment and a Stirling refrigerator simulation software, which verifies the general model as well as the principles revealed by the analytical solutions. Applicable to various types of Stirling refrigerators, the general model is able to reflect the reality in a satisfactory way and provide an approach to parametrically explore the behavior of Stirling refrigerators with the analytical solutions, which will benefit the optimization of the thermal efficiency.