To clarify the problem on the existence of many shear coefficients for Timoshenko's beam theory, the simple beam of rectangular section subjected to surface loading is analyzed by the two-dimensional elastic theory. The main results are as follows. The deflection expressed in terms of square of span is composed of not only shear deformation but also the other two deflections, which are different modes than that of shear excepting simple beams, i.e., bending deformation caused by perpendicular stress and deflection by perpendicular strain based on bending stress. By including these effects an improved deflection theory is proposed. It is made clear that Timoshenko's theory has two problems : indistinct definition of deflection and wrong inclusion of the other deformations than that caused by bending moment into the shear ones.
