A theoretical study of the high-pressure phase transition and elastic behavior in diluted magnetic semiconductors Zn 0.83 Mn 0.17 Se, using a three-body interaction (TBI) potential caused by the electron-shell deformation of the overlapping ions is carried out. The estimated values of phase transition pressure and the vast volume discontinuity in pressure-volume (PV) phase diagram indicate the structural phase transition from zincblende (B3) to rock salt (B1). The variation of second-order elastic constants with pressure resembles that observed in some binary semiconductors. The inconsistency in the deduced value of pressure derivative of second order elastic constant with the available data is attributed to the fact that we derive expressions neglecting thermal effects and assuming the overlap repulsion significant only up to nearest neighbors. The vdW interaction is effective in obtaining the thermodynamical parameters such as Debye temperature, Gruneisen parameter, thermal expansion coefficient, compressibility as well phase stability in diluted magnetic semiconductors. It is revealed that TBI model has a promise to predict the phase transition pressure and the pressure variation of elastic constants of other semiconductors as well.