In an earlier study, the author found that the melanoma incidence stayed fairly constant after 30 years of age during the first part of the 20th century in several countries. All birth cohorts, however, continued to show increasing incidence from 1957 onwards, and also after the age of 30 years. Before 1957, cell damage in skin older than about 30 years thus did not seem to be able to generate melanoma, whereas cell damage sustained later could pose a melanoma risk for much longer durations. The objective of this study was to determine whether a suddenly reduced efficiency of the cell-repair system could mathematically explain the reported increase of melanoma incidence in Sweden since 1957. A statistical distribution was used to describe the probability of cell damage developing into melanoma vs. time. Also, the probability that such damaged cells would either be repaired or killed was described as a function of time. The total probability of acquiring melanoma over time was then modelled and compared with reported data to determine the distribution parameters. The model was able to mirror the reported data both before and after the point in time at which the skin-repair system was assumed to have been impaired. This study shows that a reduced efficiency of the cell-repairing mechanisms is capable of explaining the increasing trends of melanoma incidence that we have been noticing since the mid-20th century. Other cancer types also seem to have been affected.