Cancer incidence rates are significantly different all over the world. Breast cancer is affected by many factors, the most important being genetics and lifestyle. The aim of this paper is to study the mutation mechanisms of breast cancer for Japanese women by fitting the incidence data of three high-quality population areas in Japan from 1985 to 2010. To achieve this goal, we have set up multi-stage models within the mathematical model of Moolgavkar, Venzon, and Knudson. Such models take both mutation rates and clonal expansion rates as parameters in each compartment into consideration. Based on our simulation outcomes, two to twelve driver mutations are sufficient in the pathway to female breast cancer in Japan. On the other hand, a previous study demonstrated that breast cancer in American women requires two to fourteen gene mutations to get a cancerous cell. Moreover, the 3-stage mathematical model is the optimal model as it fits clinical data very nicely for all affected cases of females in Japan and the US. The genetic instability has a prominent effect on the tumorigenesis of Japanese females caused by the first four driver mutations. The calculated results for Japanese women are compared with previous works for American women.