The paper is devoted to simply supported beams under three-point bending. The homogeneous beams with bisymmetrical cross-sections, sandwich beams and beams with symmetrically varying mechanical properties in the depth direction are studied. Analytical models of these beams are presented in detail. The shear deformation theories of the planar cross-sections of these beams are developed with consideration of the Zhuravsky shear stress formula. Based on the principle of stationary total potential energy differential equations of equilibrium of these beams are obtained. These equations are analytically solved. The deformation of the planar cross-sections of exemplary beams are analytically determined and graphically presented in figures. Moreover, the maximum deflections of these beams are derived.