Rate-distortion (RD) theory is a fundamental theory for lossy image compression that treats compressing the original images to a specified bitrate with minimal signal distortion, which is an essential metric in practical application. Moreover, with the development of visual analysis applications (such as classification, detection, segmentation, etc.), the semantic distortion in compressed images are also an important dimension in the theoretical analysis of lossy image compression. In this paper, we model the rate-distortion-classification (RDC) trade-off in lossy image compression based on the previous RD model. Specifically, the classification task is used as a representative image vision analysis task to calculate the semantic distortion. Under certain conditions, the RDC model satisfies the monotonic non-increasing and convex function properties, which are first analyzed statistically on a multi-distribution source, and then further discussed through experiments on the MNIST dataset. Our conclusions could be inspiring for human-machine friendly compression methods and emerging Video Coding for Machine (VCM) approaches.