The method of displacement discontinuity is applied in this paper to study the propagation of a vertical hydraulic fracture in a porous medium. The infiltration of fracturing fluid into a rock medium and its effect on the size of the hydraulically induced fracture are examined in this study. The equation for fluid motion inside the fracture is derived from the conservation of the fluid mass, and the equation relating the fluid pressure and the fracture opening is derived from the overall deformation of the porous rock medium. The finite element method is incorporated with the method of displacement discontinuity to obtain the solutions of the problem.