This study focuses on the issue of the best value approach (BVA) method in the public procurement and on the European experience with the implementation of the BVA method, with a focus on the use of this method in the Czech Republic. The key topic here is the effort to manage the risks of the construction project already at the stage of preparation and tender for suppliers of construction works or services, namely, for public contracts evaluated through the BVA. The findings show that public procurement tenderers often misunderstand the concept of project risk as managerial, temporal, economic, or qualitative risk. Case studies show reserves and possibilities for improvement. The goal of the study is to provide a framework for understanding and explaining the principles and methods of evaluating a qualitative criterion in the form of the risk assessment plan.