The aim of this paper is to pose and solve weight optimization problem of bar structures with constraints on faultless operation probability of a structure and constraints on design variables. Optimization method is based on a quadratic approximation of the objective function and a linear approximation of constraints on faultless operation probability of rod structures with random defects. In this paper, the initial global imperfections are considered as small independent random variables distributed according to normal law, and buckling load value is also a random variable. We study a case when under random imperfections non-multiple buckling load value is changed and non-multiple critical point type – the limit point is not changed.