The mechanisms leading to large transient growth of disturbances for the flow in a channel with compliant walls are investigated. The walls are modeled as thin spring-backed plates, and the flow dynamics is modeled using the Navier-Stokes equations linearised round the Poiseuille profile. Analysis for streamwise-invariant perturbations show that this fluid- structure system can sustain oscillatory energy evolution of large amplitude, in the form of spanwise standing waves. Such waves are related to the travelling waves which a free wall can support, modified to account for an 'added mass' effect. Simple scaling arguments are found to provide results in excellent agreement with computations of optimal disturbances, for low to moderate values of the stiffness parameter characterising the compliant surface.