Abstract: A combined micro and macro model is developed for predicting the elastic moduli of fiber reinforced composites, that is, a microscopic single fiber/matrix cylindrical element with co-focal elliptical cross sections is embedded in an infinite composite which is regarded as a homogeneous medium. The axial shear modulus has been derived in closed form by using the conformal mapping approach integrated with the Laurent expansion. The present model removes the weakness of the classical model and gives theoretical values in good agreement with experimental results.