A rate equation model of a Y‐cavity solid‐state laser with a single active medium operating simultaneously on two laser lines having a common upper level is described. Application is made to Nd3+: YAG, where the 1.06‐&mgr;m and 1.32‐&mgr;m infrared lines can be sum‐frequency mixed to produce 0.589‐&mgr;m yellow radiation. The model is used to optimize cavity design with respect to efficiency of sum‐frequency mixing.