A mechanism has been developed for assessing a company’s strategic risks and selecting the risk factors on which the risk management actions of the company must be focused. The risk factors are projections of the company’s internal and external environment which create its competitive advantages but are exposed to the most dangerous threats. The mechanism is an integral part of strategic risk controlling, the application of strategic controlling to risk management, and was built as a set of interrelated procedures which perform the selection of risk factors. The design of the mechanism is based on the integration of strategic analysis of fthe company’s value chain and failure mode and effects analysis (FMEA). This design, unlike that of the alternatives, allows maximum accounting for the majority of links and correlations among strategic goals, projections and risks. The paper elaborates on the main tasks and functions of strategic risk controlling and shows the advantages of integration of value chain analysis and FMEA in a single risk assessment mechanism. It works out the flow chart of the mechanism of assessment of the company's strategic risks. It develops the procedure of calculation of FMEA’s risk scores (risk priority numbers (RPNs)) for individual end-risks; at the level of each strategic perspective and at the level of the entire strategy. It develops the procedure of selecting the optimal strategy among the strategic alternatives using the Hurwicz minimax criterion in which strategy-level PRNs are utilized as the measures of risks. Finally, the paper works out the procedure for choosing the risk factors among strategic perspectives and develops the key tool of this procedure, the risk-factor positioning matrix. This matrix allows searching for the optimal ways and tools of risk control. The mechanism allows increasing the efficiency of risk management in strategic controlling and concentrating the management’s attention on the company’s strategic factors which are exposed to the most dangerous risks.