Joint sets within sedimentary basins are commonly interpreted to have formed by tensile failure in conditions where pore fluid pressure was elevated. Such tensile fractures are inferred to be a part of the process that relieves high fluid pressure by locally increasing rock permeability. In spite of the importance of this feedback mechanism, the detailed mechanics of hydraulic fracture genesis remain poorly understood. We describe the results of both experimental and numerical studies of hydraulic fracture genesis on the basis of an experimental protocol that combines rock extension with elevated pore fluid pressure such that the hydraulic fracture criterion is met in the sample interior. This is achieved by simultaneously dropping both minimum stress and external pore fluid pressure, inducing a large fluid pressure drop between the sample interior and its ends. Poroelastic modeling suggests that the pore fluid pressure is highest close to, but not at, the sample ends and is locally maintained at levels that meet the hydraulic fracture criterion for up to 50 s. Application of this experimental protocol to an impure sample of sandstone resulted in the generation of several hydraulic fractures subparallel to the maximum principal stress. Fracturing did not occur in a drained test on the same sample, demonstrating that the elevated pore fluid pressure was critical to fracture formation. To better understand the experimental results, we explore the role of rock permeability and storage on fracture processes using a numerical model that directly couples a lattice-Boltzmann model for fluid mechanics with a discrete element model for solid mechanics. Like the experiment, the numerical simulations produced opening mode fractures when operated to replicate the conditions of the experiment. Fractures preferentially occur in portions of the model inferred to be mechanically weak. Local fluid pressure gradients strongly influence the state of stress in the solids and thereby fracture growth. Increasing the model permeability increases fracture propagation rate, decreases sample deformation, and increases fracture spacing. Sample deformation increases, and fracture spacing decreases, with increasing overpressure. It appears that bulk forcing of the solid via fluid seepage forces is important in fracture genesis, explaining the key roles of permeability and diffusivity in the hydrofracture process.