In the usual manner relationships between exposures and densities, and some values of photographic materials derived from this relationships are obtained graphically. The author attempted to obtain these relationships and values calculatively by using mathematical models. Three mathematical models were established for photographic characteristic curves of color reversal films. After a numerical analysis of parameters employed in three models density values were calculated from values of the parameters and were compared with density values obtained by experiment. Consequently it was found that two optimum models existed for photographic characteristic curves of color reversal films. Calculatively obtained values of speed, gamma and contrast from the parameters employed in the optimum model were nearly equal to graphically obtained values. Values of the parameters and values calculated from these values did not show a violent change with changes of sampling interval on exposure.