The coupled mode equations describing parametric interactions of the electrostatic plasma surface waves and a time-oscillating pump wave are derived by retaining both the Stokes and anti-Stokes side band waves. It is shown that in the parametric approximation the coupled mode equations can be reduced to the well known form of the standard nonlinear dispersion relation of the parametric instability, whose solutions yield the purely growing mode (oscillating two-stream instability) or the oscillatorily growing resonant decay instability. The surface wave purely-growing instability is compared with the corresponding volume wave instability in terms of the coupling coefficients, and the threshold of the surface wave instability is compared to the threshold of the corresponding volume wave instability.