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 negative 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 a model gave sufficient approximation for most of photographic characteristic curves. Calculatively obtained values of speed and gamma from the parameters were nearly equal to graphically obtained values.