Abstract: By using McNamee and Schiffman displacement functions, the axial symmetry and non axial symmetry Biot consolidation equations can be reduced to a group of uncoupled partial differential equations . The governing equations of the initial problems can be established considering the initial condition of the loaded saturated half space. By utilizing the Hankel transform technique and boundary conditions of the half space surface and continuous conditions at the plane of the concentrated force acting, the displacements, stresses and pore pressure expressions can be obtained in the transform domain. The closed form initial solutions of the loaded half space can be got in terms of the inverse Hankel transforms.