The stability of the KT-2 tokamak plasma has been analyzed in the framework of ideal and resistive linearized magnetohydrodynamics. KT-2 is the Korean tokamak project that involves a large-aspect-ratio divertor tokamak with an up-down symmetric plasma cross section. First, equilibria with monotonic q profiles are investigated. Starting from four ballooning stable reference equilibria with ever broader pressure profiles and with an aspect ratio of 5.6, an ellipticity of 1.8, a triangularity of 0.6, and a total plasma current of 500 kA, the effects on the shape of the poloidal plasma cross section (ellipticity and triangularity), the aspect ratio, and the total plasma current on the ballooning and ideal and resistive external kink instabilities are studied. Also, advanced tokamak scenarios have been investigated A local profile optimization study is performed for a lower total current, i.e., I-p = 300 kA, and a magnetic field of 2 T. Next, the stability of the marginal ballooning stable equilibria with respect to so-called infernal modes is analyzed.