This paper presents the accurate prediction of static behavior of composite beams with arbitrary cross-sections. The asymptotic recursive formulation is reviewed first, where the initial three-dimensional problems are split into the macroscopic 1D problems and the microscopic 2D problems. The finite element formulation for the microscopic 2D problems is then presented in order to find the crosssectional warping solutions. The warping solutions obtained contribute the cross-sectional properties to the macroscopic 1D problems. The end effect of the 1D beam problem is also considered via the kinematic correction for a displacement prescribed boundary. The approach presented is applied to the beams with relatively complicated material distributions and cross-sectional geometry. As numerical test-beds, a three-layered sandwich beam and a composite beam with the multi-cell cross-section are taken to analyze the local deformation. A parametric study is also carried out to investigate the significance of shear deformation due to the cross-sectional orthotropic characteristics. The cross-sectional deformation is predicted based on the asymptotic framework. The accuracy of the present approach is assessed by comparing the results obtained with the 3D FEM solutions obtained by ANSYS.