An investigation of composite mechanics to investigate stress transfer mechanism accurately, a modification of the conventional shear lag model was attempted by taking fiber end effects into account in discontinuous composite materials. It was found that the major shortcoming of conventional shear lag theory is not being able to provide sufficiently accurate strengthening predictions in elastic regime when the fiber aspect ratio is very small. The reason is due to its neglect of stress transfer across the fiber ends and the stress concentrations that exist in the matrix regions near the fiber ends. To overcome this shortcoming, a more simplified shear lag model introducing the stress concentration factor which is a function of several variables, such as the modulus ratio, the fiber volume fraction, the fiber aspect ratio, is proposed. It is found that the modulus ratio is the most essential parameter among them. Thus, the stress concentration factor is expressed as a function of modulus ratio in the derivation. It is also found that the proposed model gives a good agreement with finite element results and has the capability to correctly predict the variations of the internal quanitities.