On 04.12.2015, at the seminar of “Mathematical Analysis” department “Contemporary problems and applications of harmonic analysis” candidate for a degree BSU Amrahova Aynur gave a talk on “A new constructive method for solving singular integral equations with Hilbert kernel”. The report is devoted to construction and justification of a new method for the approximate solution of linear singular integral equations with Hilbert kernel in the space of square integrable functions. In the constructive method presented in this report, the singular operator is approximated by operators preserving the main properties of this operator, and this leads to the following advantages: the removal of the strict ellipticity condition; the estimate established in this method yields more exact results in terms of the convergence rate; approximate solutions of the system of linear algebraic equations can be found explicitly and preserve the a priori well-known properties of the solution of a singular integral equation.