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In this paper we suggest and substantiate special direct methods for finding approximate solutions to integral equations of the third kind in the space of distributions. We consider a general case of location of zeroes of a coefficient. The method is based on using the Kantorovich polynomials.Keywords: integral equation of the third kind, space of distributions, approximate solution, theoretical substantiation, subdomain method. Spaces of finite functions and distributions.Let C ≡ C(I) be the space of continuous on I functions with the max-norm. According to [12], we say that a function y ∈ C belongs to the class C{m; t 0 } if there exists the Taylor derivative y {m} (t 0 ) of order m at the point t 0 ∈ (0, 1) . *