Several reports have been published on the quantitative analysis of kink formation mechanism in the output vs. current relation in stripe geometry injection lasers. The results, however, contradict with each other in basic points. In seeking for a better quantitative understanding of the transverse mode instabilities manifested by the kink formation, this paper examines basic aspects of the spatial hole-burning induced mode deformation, which is believed to cause the instabilities. Properties of the eigen functions and eigen values corresponding to the light propagation in a complex dielectric waveguide with a spatial gain and/or loss variation are examined, and an efficient approximation scheme is proposed for computing modal gain. This scheme is applied to a numerical model which approximates gain and refractive index profiles with spatially burned holes in a stripe geometry injection laser. It is found that the mode deformation induced by the hole-burning substantially affects the modal gain, and that the extent of the influence depends strongly on the refractive index contribution to the waveguiding.