The main purpose of this article is to study the behaviour of thin RC membranes under compression in one direction and tension in the perpendicular direction. The influence of the thickness on the behaviour of the concrete panel is investigated. To study the behaviour of the panels, an experimental programme was carried out. Six RC panels under pure shear were tested up to failure. As a result, new experimental stress–strain relationships of thin plates under pure shear are presented. Such relationships take into account the reduction of the compressive strength due to perpendicular tensile stresses and the influence of the thickness of the RC panels. The good experimental values obtained from this investigation validate the effectiveness of the low cost testing equipment developed for this study. This was a good achievement, because previous tests on this topic were performed using expensive equipment, which very few laboratories could afford. In general, the values obtained for the stress–strain relationships are approximately within the range proposed by other investigators. It is also shown that the strength capacity predicted by European codes is higher than that obtained from the experimental tests. The values predicted by ACI code are very conservative.