The transverse properties of unidirectional titanium matrix composites (TMCs) are dominated by the fiber/matrix interfacial properties, residual stresses and the matrix mechanical response. Nimmer et al. [1] have pioneered the research on the role of the interface when the composites are under transverse loading. In their work, a characteristic “knee” has been observed in the transverse tensile stress-strain curve of a Ti-6A1-4V/SCS-6 composite. This “knee” occurs well below the stress level at which the matrix yields extensively. The comparisons of experimental results with finite element modeling indicate that the “knee” is due to the failure of a weak interface under the transverse loading.