The waveguide modes of lambda equals 1. 3 mu m InGaAsP-InP mushroom stripe laser diodes are analyzed rigorously by means of the mode matching technique. The propagation constant and confinement factor of the fundamental TE- and TM-modes are calculated for wide ranges of the relevant laser parameters. Thereby, the cutoff condition for both modes is studied, revealing that for very narrow stripe devices (W less than 1 mu m) first the TE-mode becomes cutoff due to radiation losses of higher order lateral modes is discussed, showing that the maximum stripe width for single lateral mode guiding is higher than for comparable buried heterostructure lasers. Finally, approximate results, as obtained by using the effective refractive index approximation, are compared with the rigorous solutions, showing a satisfactory agreement only for rather large stripe widths far above cutoff.