This paper presents a recently conducted series of shear tests on reinforced concrete elements without stirrups subjected to normal forces. The main varying parameter is the level of axial compression. The tests include axial compression stresses ranging from 0 up to 85% of the concrete compression strength. Shear tests with such high level of axial compression have to the knowledge of the authors not been reported in the literature. Comparison of the test results with the design formula in the Eurocode 2 (EC2) reveals, that further enhancement beyond the upper limit imposed by the code can be obtained. The paper also demonstrates how the upper limit can be calculated by use of a plasticity based approach for shear strength prediction. The upper limit is established by considering two types of shear failure mode. It is shown that the upper limit determined in this way is in better agreement with the experimental observations. On the average - and when including existing test series with small axial compression levels - both methods considered lead to acceptable agreement with test results. It is argued, that the plasticity based method is preferable as it is based on a theoretical model and therefore is easier to extend to cases not covered by tests.