We investigate the ability of magma to propagate along preexisting fractures oblique to the least compressive stress. Relaxation of the preexisting shear stress to zero over the portion of the fracture dilated by magma (the dike) results in slip for some distance along the closed portion of the fracture ahead of the dike tip and a stress concentration near the dike tip. This could lead to the production of new tensile cracks, oblique to the parent dike, that could capture the flow. If the shear stress resolved on the fracture plane is perpendicular to the fracture front (mode I-II), the front may deviate along its entire length; if the shear stress is parallel to the fracture front (mode I-III) the front may splay into segments. For mode I-II dikes the maximum tensile stress occurs at the dike tip and is parallel to the dike. If the effective tensile stress exceeds the rock tensile strength, then the intruding magma, rather than dilating the existing fracture, is expected to propagate into a self-generated crack analogous to the "wing cracks" observed to form at the tips of pure mode II fractures. For mode I-III dikes the maximum tensile stress lies within the plane of the dike and is oriented at some angle that depends upon the far-field boundary conditions. Even if the magma pressure exceeds the ambient normal stress, it appears to be very difficult for dikes to intrude into preexisting fractures unless one or more of the following conditions is satisfied: (1) the fracture is nearly perpendicular to the least compressive stress; (2) the resolved shear stress on the fracture is small compared to the excess magma pressure (i.e., the ratio of shear to opening of the dike walls is small); (3) the effective ambient dike-normal stress is small compared to .the rock tensile strength. This indicates that it may be quite difficult for dikes emerging from midcrustal to lower crustal depths to follow faults.