Recently, new failure criteria were proposed for brittle materials to predict their failure loads regardless of the shapes of a notch or a crack in the material. This paper is to further evaluate the failure criteria for different shapes of notches and different materials. A circular hole, elliptical hole, or crack-like slit with a different angle with respect to the loading direction were considered. Double circular holes were also studied. The materials studied were an isotropic material such as polymethyl methacrylate (PMMA) as well as laminated carbon fiber composites. Both cross-ply and quasi-isotropic layup orientations were examined. The lamination theory was used for the composite materials so that they can be modeled as an anisotropic and homogeneous material. The test results were compared to the theoretical predictions using the finite element analysis with two-dimensional plane stress models. Both theoretical failure stresses agreed well with the experimental data for the materials and notch geometries studied herein.