Diffraction problems for electromagnetic waves on gratings, which consist of finite number of thing ideally conducting straps as well as on multiunit periodical gratings can be reduced to a singular integral equation of the first kind on a system of segments. In the paper a strict justification of the numerical method of solution for this equation is given, the estimates of the rate of convergence of the found solutions to exact ones and of approximate values of functionals in the solutions to exact values are obtained. These functionals are expressions of physical variables. Which characterize the scattered field.