Incidence rates of several cancers, including melanoma of the skin and breast cancer, have increased since the middle of the 20th century in Western countries. Here, we developed a model for cancer incidence over time, when considering a suddenly increased cancer risk from an environmental change. A two parameter exponential function was used to simulate cancer risk over calendar time since birth, taking into account the time lapse since the environmental change took place. The calculated incidence for all age cohorts over calendar time was used to calculate the age-standardized rates. The best fit between calculated and reported age-standardized rates was sought by parameter variation. The model was tested using reported rates for melanoma and breast cancer. The best fit was obtained when an increased cancer risk took place from 1955 and with the starting age being that of puberty. Age-standardized rates of melanoma and breast cancer were easily modeled and fit well with reported data. In addition, age-specific rates fit well with reported data without further parameter adjustments. The good fit with reported data when using this simple exponential model strongly supports the hypothesis that an environmental change in the mid-20th century was the main cause of the cancer epidemic noted after 1955. Other forms of cancer should be analyzed in a similar manner.