The fluid mechanics of viscous fluid injection into a fracture embedded in a permeable rock formation is studied. Coupling between flow in the fracture and flow in the rock is retained. The analysis is based on a perturbation scheme that assumes the depth of penetration of the fluid into the rock is small compared to the characteristic lengthw30/k, wherew0is the characteristic crack width andkis the permeability. This restriction, however, is shown to be minor. The spatial dependence of the leakage rate per unit length from the fracture is found to be linear, decreasing from the well bore to the fracture tip where it vanishes. The magnitude of the leakage rate per unit length is found to decay in time ast−1/3if the injection rate at the well bore is constant, and ast−1/2if the well bore pressure is held constant. The results cast considerable doubt on the validity of Carter’s well‐known leakage formula (Drilling Prod. Prac. API1957, 261) derived from a one‐dimensional theory. Using the simple fracture propagation model made popular by Carter, the present work also predicts that the fracture grows at a rate proportional tot1/3for a fixed well bore injection rate and a rate proportional tot1/4for a fixed well bore pressure.