We presented a finite-element-based algorithm to simulate plane-strain, straight hydraulic fractures in an impermeable elastic medium. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but an implicit strategy is needed for the crack tip to guarantee the satisfaction of Griffith's criterion at each time step. We enforced the coupling between the fluid and the rock by simultaneously solving for the pressure field in the fluid and the crack opening at each time step. We provided verification of our algorithm by performing sample simulations and comparing them with two known similarity solutions. Copyright © 2012 John Wiley & Sons, Ltd.