<p>The effect of stresses at the edge of a hole in composite plates subjected to tensile, compressive, and shear stresses was investigated. Composite plates with different mechanical properties were studied in two groups classified as unidirectional and woven fabrics. Angular stresses at the edge of the hole were calculated by means of the rotated circumferential angles (<i>α</i>) around the hole for axial and transverse loads. Unlike other loading conditions, the angular stress values were calculated for the plates subjected to shear stresses at both circumferential angles (<i>α</i>) around the hole and angle changes about rotated plate axis (<i>θ</i>). The estimated angular stress values were compared according to the maximum stress, Tsai–Hill, and Tsai–Wu failure criteria. The influences of the circumferential angle around the hole and rotated plate angle on the failure behavior of composite plates were examined in detail.</p>