In the paper a first kind singular integral equation containing a Hilbert-type double integral over the domain [0,2 π]×[0,2 π] is studied. The necessary conditions providing solvability of this equation are given. The equation studied is discretized under additional assumptions by the method of discrete singularities. The unique solvability of the discrete problem obtained is proved. The speed of convergence of the solution of the discrete problem to the exact solution of the initial singular integral equation is estimated.
