In the paper the method of discrete singularities is used for constructing a discrete mathematical model of a first kind singular integral equation with the Hilbert kernel in the case when the auxiliary conditions introduced to ensure the uniqueness of solution to the equation are given by functionals. The existence of the unique solution to the discrete model is proved and the rate of convergence of the solution of the discrete problem to the exact solution of the initial singular integral equation is estimated under some smoothness assumptions.
