The governing nonlinear equations for the hydraulically induced propagation of a circular crack in a poroelastic medium are derived. A Lagrangian formulation is utilized with the crack maximum width and radius selected as generalized coordinates. Explicit time-dependent solutions for the crack geometry and fluid pressure associated with Newtonian and non-Newtonian fracturing fluids are derived. The classical expression relating fracture width in terms of fracture radius is deduced as a special case. In addition, parameter sensitivity responses and comparison of results are presented. ¿ American Geophysical Union