Body mass index (BMI) is widely used as an index of obesity in people from the school age children to adults. However, the relationship between the change in BMI with age and the coming of menarche has not been discussed as there are few reports on the changes in BMI with age. In this study, the change in BMI with age was examined by applying the wavelet interpolation method (WIM), and a critical period for body fat in terms of the coming of menarche was estimated from the growth velocity. We investigated delayed menarche according to the influence of stress in athletes by comparing delayed menarche between athletes and non-athletes in relation to the critical period. Data were obtained from 144 female athletes in their first year at university in the Tokai area, all of whom had competed in a national sports competition in high school (athlete group). Health examination records showing these subjects' heights and weights from the first grade of elementary school to the final year of high school (1984–1995) were collected and BMI was calculated for each grade. Ages at menarche were ascertained from questionnaires. A control group of 73 non-athletes was similarly examined. The age at maximum peak velocity (MPV) derived from the growth (aging) distance curve of BMI was determined in the control group to be 11.96±0.97 years old. This age at MPV of BMI was almost the same as the age at menarche (12.11±0.93 years old). Therefore, this age at MPV of BMI is estimated to be the critical period of body fat for the coming of menarche. The interval between the age at MPV of BMI and age at menarche was 0.74±1.30 years in the athlete group and 0.15±0.81 years in the control group, so there was a significant difference (P<0.01) between the two groups. It is suggested that the delayed menarche in athletes is influenced by the stress of regular sports training.