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The paper presents a technique of quantitative assessment of probability of failure-free operation of composite structures containing an ensemble of defects in the form of delamination. This method is based on approaches of general reliability theory. The proposed method was validated relative to the assessment of reliability of a composite conical bay with multiple delaminations generated under loads at the stage of inserting the launch vehicle into orbit. The statistical dynamic problem was solved by using Monte Carlo method which was implemented by means of algorithms developed by the author in ANSYS software. Nonlinear analysis of the conical bay buckling was carried out for each implementation. Quantitative assessment of survival probability was conducted on the basis of the hypothesis of the law of Gaussian distribution of load-bearing capacity and using the graphical method of reliability calculation. Good agreement of the results obtained by both methods was noted.