Three different forms of coupling through a small hole are treated by approxi mate methods, which are justified from good physical reasoning. These are the end on coupling between a rectangular and a circular waveguides, the coupling between a TE10 mode in a rectangular waveguide and a TM120 mode in a circular cavity through a circular hole in the side wall of the circular cavity and the coupling between a TE01 mode in a rectangular waveguide and a TMmn mode in circular waveguide through a circular hole in the side wall of the latter. The purpose of this paper is to demonstrate the methods of handling problems of complicated microwave component parts. A few formulas developed in this paper are believed to be new and useful in design works.