The aim of the research was a comprehensive evaluation of concrete using the EIPI method. In the evaluation the compressive strength of concrete and its durability properties represented by sorptivity and air permeability were taken into account. Since copper slag waste with increased natural radioactivity was used in the assessed concrete, additional evaluation was carried out taking into account the influence of natural radioactivity within the performance index. Also the reference concrete, which was made without the use of copper slag waste, was evaluated for comparative purposes. In order to make the evaluation as comprehensive as possible, the concrete made with the use of three types of cement was subjected to the assessment: CEM I, CEM II and CEM III. The results show that in both approaches the best result was achieved by concrete with CEM III cement. If natural radioactivity is not taken into account in the evaluation, the best result is obtained by concrete made with copper slag waste, and if radioactivity is considered, the best result is obtained with concrete without addition of the waste. It follows from the above that although natural radioactivity has a significant impact on the EIPI evaluation result, the decisive factor is still the type of cement.