Poroelastic materials are two phase material systems consisting of a porous linear elastic solid phase filled with a Newtonian viscous fluid. Analytical investigations have demonstrated that poroelastic structures can, depending on loading and geometry, exhibit elastic response or the creep and relaxation response associated with various models of linear viscoelastic materials. This paper examines the dynamic response to harmonic loading of a disk or slab of poroelastic material. Biot’s dynamic theory for deformable poroelastic media is applied to derive expressions for a complex modulus of the material in terms of poroelastic material coefficients. Both a quasistatic analysis, accounting for dissipation but neglecting inertia, and a dynamic analysis, which neglects dissipation, are presented. For a choice of poroelastic coefficients roughly appropriate to water filled sandstone or compact bone, the poroelastic layer is shown to exhibit rubber‐to‐glass transition in a low‐frequency range. Resonance effects arising due to inertia are shown to take place at much higher frequencies than those at which changes due to dissipation take place.