[Authors] V. A. Daugavet and N. A. Tanygina [Title] The rate of convergence of the leveling method in the uniform $\Sigma$-approximation [AMS Subj-class] 49M25 Discrete approximations 41A25 Rate of convergence, degree of approximation [Abstract] The discrete uniform approximation problem of the two variable function by the sum of functions of one variable is considered. The known leveling method resulting in this problem solution is investigated. The estimation of the convergence rate under certain assumptions is obtained. [Comments] LaTeX, Russian, 6 pp. [Contact e-mail] Daugavet@VD3999.spb.edu