Abstract: Through introducing the axisymmetric potential function of a poroelastic half space, the dynamic Green’s function of concentrated pore fluid pressure is given. Firstly, an auxiliary surface is introduced along the location of the source, then through the condition of the free surface of the poroelastic half space and the continuous condition of the auxiliary surface. The coefficients of the potential function are obtained. Then the dynamic response of the three-dimensional poroelastic half space is obtained by using the relation between the potential function and the displacements and stresses. Two boundary drainages are considered: the drained surface and undrained surface and the effects to the displacements and pore pressure of the porosity are discussed, and some useful conclusions are given.