Initial findings on the load-bearing behaviour of carbon reinforced concrete components under uniaxial compressive stress are available, however multi-axial stress states are of particular relevance for an application in construction practice. It is known from steel reinforced concrete constructions that transverse tensile stresses lead to a reduction in the compressive strength, although there is still no international agreement on the actual reduction. In this paper we investigate the boundary conditions under which carbon reinforced disc shaped specimens can be tested under combined compressive and tensile loading. This includes the anchoring of the carbon yarns required for the tests in limited space conditions as well as the influence of the loading regime - proportional or sequential - and the manufacturing process - laminated or casted - on the test results. Finally, an outlook on the following investigations is given.