This article considers weakly singular, singular and hypersingular integrals which arise when the boundary integral equations (BIE) are used to solve problems in the theory of elasticity and fracture mechanics. For their regularization, an approach based on the application of the Gauss‐Ostrogradskii and the Green theorems has been used. The expressions, which allow an easy calculation of the weakly singular, singular and hypersingular integrals for any convex polygon, have been constructed. Such an approach may be generalized easily and applied for the calculation of multidimensional integrals with various singularities.