Pressure-induced structural phase transitions in Pb 1-x Mn x S (0 < x < 0.05), from the rocksalt (B1) to the CsCl (B2) type phase, have been calculated. The present study of the phase transition is based on the three-body potential (TBP) approach, which includes long-range as well as short-range interactions. The long-range part consists of a Coulomb and three-body interactions, whereas the short-range part includes the van der Waals and overlap repulsive interactions. In order to strengthen the significance of our results and verify the presence of intermediate orthorhombic phase during B1 to B2 structural transition in the host binary compound PbS we performed first principles full potential linear muffin tin orbital approach and provided a good support to our TBP results. Our first-principles calculations, based on the full potential muffin tin orbital (FPLMTO) method, successfully predicts the TlI type phase and supports the TBP results.