An approximate method is developed to investigate the interlaminar stresses near the free edges of beam-type composite laminate structures subjected to out-of-plane shear/bending. The method is based upon admissible function representations for in-plane stresses that contain a linear variation in the longitudinal direction. Closed-form solutions of all stress components are sought by minimizing the complementary energy with respect to the unknown functions. The resulting solutions satisfy the stress equilibrium, compatibility, and all of the boundary conditions. Numerical examples are given for both cross-ply and angle-ply laminates. It is found that interlaminar stresses under the shear/bending, particularly those for angle-ply laminates, may exhibit substantially different characteristics than under uniaxial loading or under pure bending.