Crevasses form in response to tensile stresses in glaciers and ice sheets. It has been widely assumed that crevasses initiate at, or near, the surface of the ice, from starter cracks up to a few centimeters long. If the tensile stress is sufficient, these cracks propagate downward into the ice to form a crevasse, until the weight-induced lithostatic stress prevents them penetrating deeper. We present ground-penetrating radar data acquired on the Rutford Ice Stream, Antarctica, which indicate that crevasses occur at depths of several meters beneath the ice surface and were formed in areas where surface crevassing is absent. The data support the hypothesis that these are examples of subsurface crevasse formation. Using linear elastic fracture mechanics (LEFM), we investigate the feasibility of crevasse initiation at depth. We consider the initiation of an isolated crevasse from a subsurface crack, subject to a dynamic tensile stress which results from deformation associated with ice movement and a weight-induced lithostatic stress. The LEFM approach allows us to estimate ainit, the minimum length a crack must be before crack propagation will occur. In earlier models of crevasse formation, it was assumed that the dynamic tensile stress is constant with depth. We consider a more realistic scenario, where the dynamic tensile stress varies with depth, in such a way that the tensile strain rate remains constant. We show that in this scenario, crevasse initiation from centimeter-scale starter cracks is feasible at depths of 10--30 m, as well as at the surface. At present, the formulation of a reliable predictive model is limited by an incomplete knowledge of the mechanical properties of firn. In previous studies, the depth of buried crevasses has been used to estimate the time elapsed since ice was exposed to higher stresses and different flow regimes. In the light of the results presented here, those estimates may need to be reviewed.