The structural stability of rare earth nitrides REN (RE=Ce,Pr,Nd) is investigated among three cubic structures, namely, NaCl (B1), CsCl(B2) and zinc blende (B3). It is found that NaCl structure is the most stable structure for all the three nitrides. On increasing the pressure, structural phase transition from NaCl (B1) to CsCl (B2) phase is predicted in CeN and NdN at the pressures of 88GPa and 36.5GPa while NaCl (B1) to zinc blende (B3) phase transition is observed in PrN at the pressure of 68GPa. At normal pressure, all the three nitrides are stable in the ferromagnetic state (FM) with cubic NaCl (B1) structure. The calculated lattice parameters and bulk modulus values are in good agreement with experimental and other theoretical values. Electronic structure reveals that PrN and NdN are half metallic while CeN is metallic at normal pressure. Ferromagnetism is quenched in CeN and PrN at the pressures of 152GPa and 121GPa respectively. The positive values of elastic constants indicate that all the three nitrides are mechanically stable in NaCl Phase. It is found that all these nitrides are ductile and anisotropic in nature.