In this paper by using of modified shear-lag model and superposition technique, the stress concentration factor in a unidirectional composite lamina with angled and staggered cracks is investigated. Unlike classical shear-lag model, in modified model, both the fiber and matrix are able to sustain axial loads. For a unit cell of fiber and matrix , the differential-difference equations of equilibrium were derived and solved for displacements and stress fields within the lamina. For a total fiber N and row of r, number of break fiber ,by superposition technique, The maximum stress concentration factor of lamina with angled and staggered breaks was calculated. Results show that the classical shear-lag model can not predict the stress concentration factor accurately when value of Matrix-to-Fiber moduli ratio is increased. In glass-epoxy lamina with staggered and angled cracks, the maximum stress concentration factor decreases by 39% and 43%, respectively, versus the aligned fiber breaks. By increasing the Matrix-to-Fiber moduli and Matrix-to-Fiber volume fraction ratios the maximum stress concentration factor decreases. As Em/Ef approaches to zero, results have a good agreement with primary shear-lag model.