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Limit states of simple, spatial, non-linear models of structures with two degrees of freedom are considered. Geometric and material imperfections are taken in the form of random variables. The simulation of these random variables and the Monte Carlo technique are employed. Two possibilities in the assessment of the reliability of structures are presented: I) Simulation of random imperfections and the Monte Carlo operation give as a result a histogram of the limit loads. Assuming that the probability distribution of the applied load is known, the structural reliability can be obtained according to the exact formula. 2) In order to obtain the histogram of the limit state of the structure, the values of the applied load are also simulated at every Monte Carlo step. The factor which amplifies the load responsible for the structure failure is derived. The set of all these factors leads to the model reliability calculation. The estimation of the limit state of an imperfect structures can be described as a transformation of random input data into random output results. In the transformation operation the non-linear operator of the model under considerations is of the greatest significance. The effects of stable and unstable operators are discussed.