Questions related to accidents prevention based on non-destructive control of critical defects, functioning dangerous technical systems with high wear levels, as well as to substantiation of measures for step-by-step risk mitigation of the specified systems after their stop have been considered. For security upgrade relating to operation of potentially dangerous technical systems under resources restrictions are applied measures for prevention of accidents, mainly, the non-destructive control (NDC) of these systems technical condition without their stop. So, complexes of NDC-methods are applied for fault detection of functioning long distance pipe lines and industrial chimneys. The defects elimination process, and recovery works on the stopped idle systems can be considered as stage-by-stage risk management implementation. With increase of specified measures’ costs the accidents damage risk mitigation is reached. At the same time modified to year expenses representing the sum of presented expenditures related to risk mitigation measures and the presented accidents damage at some cost value for risk mitigation take up minimum value. Further expenses level increase with minimum cost is not compensated by the level of prevented damage. Searching of the specified expenses level for accidents risk mitigation with minimum cost is an optimization problem on minimization of the modified to year risky expenses. In this work has been offered a risk management algorithm scheme at operation of such potentially dangerous technical system as a functioning industrial reinforced concrete flue.