The structural, electronic and elastic properties of orthorhombic and hexagonal Mo2C were investigated using first principles with a pseudopotential plane-wave method. The results for the formation enthalpy of these compounds indicate that Ortho-Mo2C can form more easily than Hexa-Mo2C. The calculated electronic structure indicates that the bonds of Mo2C have both covalent and metallic properties. The stability of multicomponent carbides (Mo,M)2C (M = Cr, Nb) in both orthorhombic and hexagonal form was also investigated.