We have analyzed the amplification of a signal wave in the optical parametric interactions of the pump, signal, and idler waves in planar waveguides, with the pump wave being Cerenkov radiation. Based on the coupled-mode theory, we have derived the first-order coupled-mode differential equations for no pump depletion. The equations can easily be solved numerically. The approximate analytical and numerical solutions of the equations show that the signal wave can be amplified parametrically.