The influence of layer waviness on the stress state and failure pressure of thick cross-ply composite cylinders loaded by external hydrostatic pressure is studied. Layer waviness is idealized as a single isolated region of waviness in an otherwise perfect cylinder. The waviness occurs in only the circumferential direction and is assumed to extend indefinitely in the axial direction. Waviness is assumed to occur because particular circumferential layers experience local radial displacement during consolidation, resin richness and resin depletion occurring on either side of the locally displaced layers. Stresses are computed by using a finite element analysis which models the isolated region of waviness in the cylinder on a layer-by-layer basis. Some details of the model are discussed; the model accounting for a range of amplitudes of waviness, a range of cylinder radius-to-wall thickness ratios, and whether the isolated waviness is located near the inner radius or near the outer radius of the cylinder wall. The paper illustrates the behavior of the three primary stresses, namely interlaminar shear, interlaminar tension, and fiber-direction compression, all of which are important to failure. Pressure capacity is determined by applying the maximum stress failure criterion. It is shown that interlaminar shear, while absent in the perfect cylinder, can be responsible for a 50% reduction in pressure capacity relative to the wave-free perfect cylinder. Also it is shown that fiber-direction compressive stresses are increased by the presence of waviness, and that interlaminar normal tensile stresses caused by the waviness are potentially responsible for failure.