Background: Numerous studies have been conducted on composite materials, concerning development at the microscopic scale. In addition, the elaboration of composites at relatively high temperatures leads to very localized residual stresses in the fiber and the matrix in the neighborhood very close to their interface. These shear stresses put the fiber in compression and the matrix in tension. The objective of this work is to analyze the behavior of cracks initiated in the interface of a unidirectional ceramic fiber-reinforced composite and to study, in three dimensions by the finite element method, the effect of these constraints on the crack behavior appeared in this composite. This behavior is analyzed in terms of stress variation intensity factors in modes I, II and III. The effect of several parameters has been studied.