The dynamic responses of squeeze films to fluctuating loads are compared for the cases of rigid, elastic, and viscoelastic bounding surfaces. Unexpected and interesting differences are observed. These include the oscillatory response of indenter position to a non-negative fluctuating load and the decaying load versus time response to a prescribed indenter trajectory which remains constant over a period of time. Practical implications of these responses are noted. The transient analysis procedure, while general, is applied to a simple geometrical and physical model: an isoviscous Newtonian fluid squeezed between circular, initially flat, three-element viscoelastic Winkler solids. Surface deformation rate and film rupture are incorporated. The fully implicit numerical method utilizes a generalized Newton scheme together with finite element spatial discretization.