Synthetic Aperture Radar (SAR) is highly susceptible to Radio Frequency Interference (RFI). Due to the performance limitations of components such as gain controllers and analog-to-digital converters in SAR receivers, high-power interference can easily cause saturation of the SAR receiver, resulting in nonlinear distortion of the interfered echoes, which are distorted in both the time domain and frequency domain. Some scholars have analyzed the impact of SAR receiver saturation on target echoes through simulations. However, the saturation function has non-smooth characteristics, making it difficult to conduct accurate analysis using traditional analytical methods. Current related studies have approximated and analyzed the saturation function based on the hyperbolic tangent function, but there are approximation errors. Therefore, this paper proposes a saturation interference analysis model based on Bessel functions, and verifies the accuracy of the proposed saturation interference analysis model by simulating and comparing it with the traditional saturation model based on smooth function approximation. This model can provide certain guidance for further work such as saturation interference suppression.