The purpose of this paper is to describe experimental and numerical investigations focussed on the shock wave modification induced by a dc glow discharge. The model is a flat plate in a rarefied Mach 2 air flow, equipped with a plasma actuator composed of two electrodes. The natural flow without actuation exhibits a shock wave with a hyperbolic shape. When the discharge is on, the shock wave shape remains hyperbolic but the shock wave is pushed forward, leading to an increase in the shock wave angle. In order to discriminate thermal effects from purely plasma ones, the plasma actuator is then replaced by an heating element.