The electronic structure and elastic properties of the 4d transition metal carbides MC (M = Y, Zr, Nb, Rh) were studied by means of extended H$ddot{u}$ckel tight-binding band electronic structure calculations. As the valence electron population of M increases, the bulk modulus of the MC compounds in the rocksalt structure does not increase monotonically. The dominant covalent bonding in these compounds is found to be M-C bonding, which mainly arises from the interaction between M 4d and C 2p orbitals. The bonding characteristics between M and C atoms affecting the variation of the bulk modulus can be understood on the basis of their electronic structure. The increasing bulk modulus from YC to NbC is associated with stronger interactions between M 4d and C 2p orbitals and the successive filling of M 4d-C 2p bonding states. The decreased bulk modulus for RhC is related to the partial occupation of Rh-C antibonding states.