An effective way to achieve High Resolution and Wide Swath (HRWS) imaging capability is the multi-channel technique in azimuth. Improved resolution and swath can dramatically increase the volume of echo data in the SAR system. However, the onboard data storage and data-transmission bandwidth are limited, so data compression technique is typically used to reduce the volume of echo data. To study the effect of raw data compression on the azimuth multi-channel SAR system, in this paper, we establish a multi-channel SAR signal model based on data compression. We then derive and analyze the effects of data compression on the Signal-to-Noise Ratio (SNR) scaling factor of the multi-channel SAR system and quantization noise. Finally, we verify the validity of the proposed model and analysis results using simulation and real data and discuss the effect of data compression on the Peek-to-Ghost Ratio (PGR). The results of this paper provide an important theoretical basis for the choice of compression method in the multi-channel SAR system.