If strip transmission lines are enclosed in a conducting shield, the shield acts as a waveguide and spurious waveguide modes, which interfere with stripline transmission, are excited. A waveguide mode suppressing structure is disclosed which selectively suppresses the waveguide modes over a certain frequency range and also physically provides support for a dielectric substrate. The structure has at least one groove, having an approximate electrical depth one-quarter of the wavelength of the stripline operating frequency, positioned in the shield side wall. This structure provides suppression without restricting cross sectional dimensions of the channel, thereby allowing more circuits on a substrate and greater freedom in strip transmission line circuit design than in the prior art. Additionally, at least one resistive thin film may be deposited on the dielectric substrate in the vicinity of the groove to increase suppression capability.