The elastic properties of lead sulfur selenium are studied using first-principles calculations. The geometry optimized structural parameters for PbS0.5Se0.5 under different pressures are listed. The lattice parameter increase with increasing pressure, but enthalpy is constant. However, parameter B and Y decrease and parameter S increase with increasing pressure. The elastic constants satisfy the traditional mechanical stability conditions for these ternary mixed crystals. The elastic modulus as two functions of pressure from 0 - 10 GPa are obtained. The calculated elastic constants Cij decrease but with different rates under increasing pressure.