The complementary functions method (CFM) is used to investigate the static behavior of laminated composite frames consisting of straight and/or curved members of variable cross section. The Timoshenko beam theory (TBT) is used to obtain the set of the governing equations. The fifth-order Runge-Kutta (RK5) algorithm is employed in the solution process of initial value problems via the CFM. A computer program is substantially coded in Fortran on rigidity matrix based on the CFM to acquire the rigidity matrices and load vectors of these structural elements. With the help of the suggested method, the influences of the symmetric layer stacking sequence, the ratio of E-1/E-2, and various boundary conditions on the nodal displacements and element end forces of the considered frames are investigated. Carrying out the static behavior of laminated composite frame systems which contain straight and circular axis elements for the first time by using the CFM is the novelty of this study. Verification and accuracy of the suggested scheme are intently performed through the comparison of the present results with those of the finite element method. The effectiveness of the method and good agreement of the results are observed.