An approximate elasticity solution is developed for the response of the finite-width, angle-ply composite laminate under uniform axial strain. The solution yields components of the displacement vector, strain tensor, and stress tensor in the form of sinusoidal-hyperbolic series. Results of the approximate solution are compared to numerical solutions of the exact equations for four-layer, symmetric laminate geometries. The nature of the boundary disturbance in the eight-layer laminate is also examined by the approximate solution.