Average values of the mechanical properties of the interphases in a unidirectional fiber-reinforced composite have been obtained using a combined experimental and numerical approach. The effective elastic constants of the composite have been determined from measured values of the bulk wave velocities in the composite. Using known values of the mechanical and geometrical properties of the fibers and the matrix, the composite has been modeled by a hexagonal array of fibers in a matrix, and the interphases have been described by a spring-layer model. For known values of the interphase properties, the effective elastic constants have been calculated by carrying out finite element calculations over a representative cell. When the interphase properties are unknown, the finite element procedure has been used in an iterative mode to obtain the interphase properties by systematic comparison between calculated and measured values of the composite's effective elastic constants.