The flaws that exist in rock masses may lead to crack propagation and instability of rock masses. Epoxy resin is often used to fill in flaws and to reinforce the fractured rock masses. Previous studies on the combined influence of grouting with epoxy resin and flaw geometry (flaw thickness and inclination angle) on the strength and failure pattern of rock masses are rare. In this research, rock-like specimens with an unfilled flaw having different geometries were fabricated and tested under uniaxial compressive load under both unfilled flaw and epoxy resin filled flaw conditions. The specimens had flaw thicknesses of 1 mm, 2 mm, and 3 mm and flaw inclination angles of 0°, 30°, 45°, 60°, and 90°. The experimental results reveal that for the specimens with an unfilled flaw the UCS drops in the range of 7–17% as the flaw thickness increases, but failure patterns do not change as the flaw thickness increases. UCS also dropped as the flaw inclination angle increased from 30° to 60° and then increased when the inclination angle increased from 60° to 90°. For the specimens with an unfilled flaw, the minimum UCS of about 62% of the intact UCS of the model material was obtained for 60° flaw inclination angle. For the specimens grouted with epoxy resin, as the flaw thickness increases, the UCS decreases in the range 16–21% when the flaw inclination angle is 30°, 45°, and 60°; but the UCS changes negligibly for the flaw inclination angles of 0° and 90°. For the specimens with a grouted flaw, the minimum UCS of about 74% of the intact UCS of the model material was obtained for flaw inclination angle of 60°. For grouted flaw, a maximum UCS almost equal to the intact UCS of the model material was obtained for 0° and 90°. The failure patterns of these grouted specimens are affected by both the flaw thickness and flaw inclination angle. The strengthening factor Ds is used to indicate the grouting effect; a larger Ds represents a stronger grouting effect. When α = 0° and 90°, Ds of a specimen with a larger flaw thickness is larger than that of a specimen with a smaller flaw thickness. When α = 30°, 45°, and 60°, the thickness has little influence on the Ds in this angle range. Ds of the specimens with the flaw inclination angle of 0° is much higher (22% to 43%) than that of the specimens with the flaw inclination angles of 30°, 45°, 60° and 90° (14% to 24%). For the specimens with the flaw thickness of 1 mm, 2 mm, and 3 mm, Ds increases slightly as α increases from 30° to 60°. The effect of grouting on the failure patterns and strength of the specimens has a close relationship with the flaw thickness and flaw inclination angle. The above conclusions are new findings, which can provide useful information for estimating the failure mode and grouting effect of fractured rock masses grouted with epoxy resin.