A model for the calculation of the inelastic contribution to the low-bias electron transport in molecular junctions is presented. It is an extension to the inelastic case of the Green's function approach to the calculation of the conduction of such systems. The model is suited for the calculation in the off-resonance regime (where molecular levels are far from the Fermi energy) and in the low bias limit, a typical situation encountered in inelastic electron tunneling measurements. The presentation of a general model is followed by the introduction of several approximations that make the calculation feasible for many systems of interest. Ab initio calculations of the vibronic coupling that leads to inelastic contribution to the conductance are performed for several molecules (butadiene, biphenyl, dipyrrole, and dithiophene), representative of possible molecular wires. The role of inelastic conduction is then quantified without empirical parameters and the vibrational modes that dominate the process are identified. The situations where the inelastic mechanism is particularly relevant are considered. The limits of this approach for the resonant case are also discussed. (C) 2003 American Institute of Physics.