This work aims to analyze the random response of the steel hall under dynamic wind excitation. Its mainframes have been modeled as tapered I-beams and the numerical model has been introduced into the FEM system ABAQUS. Finite beam elements with quadratic shape functions have been used including 7 degrees of freedom capturing a warp of all the I-beams. Deterministic dynamic analysis has been performed with Hilber-Hughes-Taylor algorithm and recovered structural responses in 10 minutes time interval has been recovered for further structural response approximations in polynomial form. The Iterative Generalized Stochastic Perturbation Technique of the 10th order has been applied to determine random expectations and higher-order probabilistic characteristics of structural responses, and this method have been contrasted further with the Monte-Carlo Simulation estimation and with the Semi-Analytical Method integration procedures. All probabilistic calculus including reliability analysis and Least Squares Method approximations and their statistical optimization have been programmed in computer algebra software MAPLE 2019.