An analytical model was developed to predict the mechanical response to axial loading of oriented fiber composite materials containing a third (dissimilar) material at the fiber-matrix interface. The model approximated the fiber composite geometry by three concentric, but integral, cylinders. Both a totally elastic and an elastic-plastic analysis of the three-component cylinder demonstrated that transverse stresses, with the signs and magnitudes depending upon the elastic and plastic characteristics of the components, developed during axial loading. Tensile transverse stresses, which could drastically reduce the axial properties of the composite if a brittle layer existed at the interface, were shown to result from various combinations of component properties. The internal stresses predicted for the composite model were verified experimentally by testing three-component composite cylinders of maraging steel-copper-maraging steel and Berylco-copper-Berylco in tension.