In this paper, an upper bound of the longitudinal elastic modulus of unidirectional fibrous composites is proposed according to strength of materials approach, on the premise that the fiber is much stiffer than the matrix. In the mathematical derivations, the concept of boundary interphase between fiber and matrix was also taken into account and the main objective of this work is the attainment of an upper bound for the interphase stiffness with respect to fiber concentration by volume. The novel element here is that the authors have not taken into consideration any specific variation law to approximate the interphase modulus. The theoretical results arising from the proposed formula were compared with those obtained from some reliable theoretical models as well as with experimental data found in the literature, and a satisfactory agreement was observed.