This paper presents time-dependent response of an elastic circular plate in a multi-layered poroelastic medium subjected to axisymmetric vertical loading. The plate-half space contact surface is smooth, and either fully permeable or impermeable. The interaction problem is analyzed by using a variational approach and the formulation is derived in the Laplace transform domain. Time domain solutions are obtained by using a numerical Laplace inversion scheme. Selected numerical results are presented to demonstrate the influence of plate rigidity, hydraulic boundary condition, types of loading and layer configuration on time-dependent response of an elastic circular plate.