A systematic unified theoretical analysis for Europium Sulphide (EuS) have been investigated by a lattice dynamical model which includes the effect of three-body interaction (TBI) in the framework of second neighbour rigid shell model (SNTRSM) and second neighbor rigid ion model (SNTRIM). The significance of these two approaches thus obtained, have been applied to study the elastic constant of first and second order, cauchy discrepancy, pressure derivatives, anhormonic properties and high pressure phase transition study of Europium sulphide (EuS) by the supplication of TRSM (three-body force shell model) and TRIM (three-body force rigid ion model). It is concluded that our theoretical results predicted by SNTRSM on phonon dynamics and derivable properties will be very much close to their measured data. These are probably the first reports of its kind and they will certainly help the experimental workers to analyze their data in future.