This paper examines the variable thermal conductivity influence on MHD flow past a thermally stratified stretching cylinder with heat source or sink. The governing partial differential equations of the flow field are converted to a system of non-linear coupled similarity ordinary differential equations. Employing Shooting technique followed by Runge-Kutta method, the system is solved numerically. The effects of the various physical parameters countered in the flow field on the velocity, temperature as well as the skin friction coefficient and the rate of heat transfer near the wall are computed and illustrated graphically.