Results of a study to investigate the influence of non-uniform stress fields on the failure strength of rocks are presented. Three rock types, Westerly granite, Nugget sandstone, and Tennessee marble, were tested to failure in unconfined tension, torsion, and bending tests, and in triaxial compression and extension tests. Specimens were prepared with notches of various sharpness to vary the intensity of the stress gradients in the specimens. Analyses were performed to determine how the magnitude of the stress varied across the specimen. Two significant experimental observations were made. First, the fracture stress was insensitive to the notch configuration for all rocks tested. Second, local stresses existed in the specimens near the crack tips significantly above the stress required to fracture the rock in a uniform stress field. A preliminary correlation of the increase in strength exhibited by a specimen in a non-uniform stress field is presented based on a critically stressed distance that varies with the maximum stress.