This paper considers the steady-state vertical vibrations of a rigid circular disk embedded at a "nite depth below the free surface of a poroelastic medium. Biot's elastodynamic theory for porous media is used in the analysis. General solutions for axisymmetric poroelastic "elds are obtained by using Hankel integral transforms. Analytical solutions for in#uence functions corresponding to four types of buried axisymmetric excitations are derived. The embedded disk problem is fomulated in terms of a set of coupled integral equations for unknown traction and pore pressure jumps across the disk. The kernel functions of the integral equations are the in#uence functions corresponding to buried vertical, radial and pore pressure ring loads. The system of integral equations is solved numerically by discretizing the disk into several concentric annular rings. Selected numerical solutions for displacements, vertical stress and pore pressure due to a buried fully #exible disk (uniform pressure) are also presented. The vertical compliances of a rigid disk are examined for di!erent depths of embedment, poroelastic materials and hydraulic boundary conditions. Solutions for traction and pore pressure jumps are also examined. The present results are useful in the study of dynamic response of embedded foundations and anchors in poroelastic soils.