Abstract: A higher order shear deformation theory based on global local displacement hypothesis is proposed.This theory fully satisfies the geometric and stress continuity conditions at interfaces and free shear traction conditions on the top and bottom surfaces.It is found that a so called global local superposition technique could be used for expressing the laminate theories in an explicit manner to retain the advantage of numerical efficiency.Based on the superposition technique,the individual terms are identified.It is concluded that not only the completeness of the terms,but also the inclusion of as many terms as possible, are important to a laminate theory.A three nodes triangular element based on this theory is also proposed.The numerical examples show that the higher order shear deformation theory can describe accurately the shear deformation and this displacement element can calculate accurately not only the global displacements but also the interlayer shear stresses.