Methods of mathematical statistics and probability theory are deeply studied and can be successfully used as a means of assessing the stability of the functioning of informatization objects (OI) in the normal conditions of its application. The standard conditions allow us to obtain representative descriptive statistics, evaluate the corresponding probabilistic characteristics and apply the methods of probability theory. Ensuring the reliability of the functioning 
 of OI in normal conditions is provided by effective operational cover. However, for massive computer attacks (MCA), the dynamics of OI behavior and the development of the situation are unpredictable, and the events themselves are rare, which does not allow the above methods to be correctly applied. The significance and novelty of the study lies in the positive assessment of the applicability of the Monte Carlo method for assessing the survivability of the restored OI, which is subject to MCA and has temporary redundancy (recoverability). Assessing OI survivability is considered from the point of view of the need to implement a methodology for ensuring the risks of information security associated with MCA. The statement of the problem, the modeling algorithm, and solution examples are given, on the basis 
 of which it is possible to recommend the Monte Carlo method for solving the set problem. The enlarged stages of the statistical modeling procedure are given, the solution of the actual problem of assessing OI stability for MCA conditions is described. The obtained partial conclusions may be of interest for planning further scientific research in the direction of improving the processes of decision making to ensure the sustainability of the functioning of OI in conditions of targeted aggressive influences. A case of statistical modeling is given, taking into account possible scenarios for applying MCA and interpreting the simulation results