We have performed a series of laboratory tests to study the propagation of a hydrofracture into and through an interface between two rock-like materials. Test specimens were prepared by embedding sandstone tablets (lenses) in blocks of gypsum cement. These blocks were hydrofractured under true triaxial loading conditions, at a constant fluid injection rate. The injection path and applied state of stress were designed so that we obtained a single-wing fracture, propagating in a place perpendicular to the interface. Fracture growth was tracked via extension failure of fine tungsten wires embedded in the gypsum. After testing, the blocks were dissected and the extent of fracturing and fluids leakoff were recorded. In each test, the hydrofracture propagated into and through the discontinuity. Pressure-time and fracture tracking data were consistent for all tests. Distinct step increases on the pressure-time record were also noted in all tests, and are related to the interaction of the hydrofracture with the sandstone lens. All the fracture showed step-crack behavior upon entering or exiting the sandstone tablet. In addition, a finite element model was used to simulate the experiments. Pressure-time records from the model and the experiments compare favorably. 8 refs., 9 figs.