A graduation thesis investigation of "Bolshoi" arena in Sochi is presented in this article. A method of F.E. modeling of a dimensional stadium roof model is presented. Stress and strain state of the roof's supporting framework is analyzed. The contribution of individual loadings is rated. The most dangerous loading is shown. A two alternative framework of a roof proposed and analysed using numerical method.The results of the metal consumption optimisation are presented. The most effective structural scheme is shown.