It is known experimentally that an imperfectly expanded rectangular jet from a thin-lip convergent nozzle emits only a single dominant screech tone. The frequency of the screech tone decreases continuously with an increase in jet Mach number. However, for a supersonic jet issued from a bevelled nozzle or a convergent-divergent nozzle with straight side walls, the shock cell structure and the screech frequency pattern are fairly complicated and have not been predicted before. It is shown that the shock cell structures of these jets can be decomposed into waveguide modes of the jet flow. The screech frequencies are related to the higher-order waveguide modes following the weakest link screech tone theory. The measured screech frequencies are found to compare web with the predicted screech frequency curves.