Abstract: Solutions of elastic stresses of a single fiber-reinforced composite under an applied load parallel to the axis of the fiber are given.The radial distribution of the axial stress in the matrix,the distribution of the axial stress in the fiber and that of the interfacial shear stress along the fiber are presented.And the effects of the fiber-to-matrix elastic modulus ration on the maximum fiber axial stress and the maximum interfacial shear stress are studied.Also,a comparison between the present study and the existing works is made.Finally,this study gives the solutions of elastic stresses of a multi-fiber-reinforced composites.