Normal mapping is an essential rendering technique in 3D computer graphics to express detailed wrincleness and bumpy texture of the surface. As the normal mapping is increasingly utilized, compression of normal maps is becoming a significant issue. The problem is there is no quality evaluation model for lossy compressed normal maps. Therefore, in this paper, we have developed a mathematical model to analyze the characteristics between lossy compressed normal maps and 3D images rendered with them. By calculating averages of the parameters which cannot be defined uniquely and by introducing some assumptions, the model has been expressed in a simple form. The validity and generality of our model have been demonstrated by experiments. The model proposed in this paper will be helpful for deciding normal map compression strategy considering the target quality of the rendered 3D images.