From Maxwell's equations in an orthogonal curvilinear coordinates system, a strict derivation of mode coupling coefficients among TE<sub>n0</sub> rectangular waveguide modes is given, obtaining the general and explicit formulas of the coupling coefficients. Theoretical design methods and a useful set of expressions for several kinds of overmoded rectangular waveguides are reported, which enable engineers to quickly design these types of waveguide bends. Firstly, a 90° <i>H</i>-plane bend was investigated to change the wave propagating direction to its perpendicular direction for a certain purpose. Its transmission efficiency of TE<sub>10</sub> mode is 99.9% at 9.5 GHz, with bandwidth (for transmission efficiency >; 95%) of 8-12 GHz. Secondly, a strict and explicit derivation of mode conversion efficiencies of two mode converters, i.e., dual-bend and tri-bend TE<sub>20</sub>-to- TE<sub>10</sub> converters, are proposed. Both of them have similar conversion efficiency of 99.9% at 8.5 GHz with bandwidths (for mode-conversion efficiency >; 95% ) of 7.98-9.07 and 8.09-8.97 GHz, respectively. All of the theoretical models presented in this paper are verified by the finite-element simulations. We also experimentally show the performances of these devices, which are sufficient to demonstrate the validity of the theoretical models.