The effect of thermal radiation on flow and heat transfer of Maxwell fluid over a stretching surface with variable thickness embedded in a porous medium is considered. The governing non-linear PDE are transformed into a non-linear ODE by using a similarity transformation. These equations were solved numerically with fourth/fifth-order Runge-Kutta method. A comparison of obtained numerical results is made with the previously results in some special cases and excellent agreement is noted. The effects of elasticity, radiation parameter, porosity parameter, wall thickness parameter, and thermal conductivity parameter on the velocity and temperature profiles are presented. Moreover, the skin-friction and Nusselt number are presented.