ABSTRACT This approach present improved higher-order layer-wise theory for the investigation of flawlessly wedged sandwich-composite beams with general laminate configurations. Our analysis incorporates the continuity assumption of interlaminar shear stresses and in-plane and flexural displacements between interfaces. In addition, interlaminar shear stresses are constrained using the Lagrange multiplier technique by introducing new unknown variables. These unknown variables are expressed with interlaminar strain energy, assuming that the strain energy is continuous throughout the overall thickness of the beam. To govern the newly introduced and other unknown variables, the total potential energy (TPE) is minimised using variational calculus. The numerical analysis results show that our approach provides enhanced accuracy to examine sandwich-composite beams.