A new strong mathematically rigorous and numerically efficient method for solving the boundary value problem of scalar wave diffraction by an infinitely thin circular ring screen is proposed. The method is based on the combination of the Orthogonal Polynomials Approach and the ideas of the methods of analytical regularization. As a result of the suggested regularization procedure, the initial boundary value problems was equivalently reduced to the infinite system of the linear algebraic equations of the second kind, i.e. to an equation of the type ( I + H ) x = b , x, b E 1, in the space I, of square summable sequences. This equation was solved numerically by means of truncation method with, hi principle, any required accuracy. Scalar wave diffraction by the perfectly conducting circular ring which is infinitely thin on z=O plane and is surface of the kind S=((z, r, cp): z=O, rE [a, b] , c p~ [-n,n]) in polar coordinate system (z, r, cp) is considered. The method based on combination of Orthogonal Polynomials approach (see Ref. [ 1-21) with analytical regularization technique analogous to Ref.[3-51. As it is well-known, the diffraction problem can be equivalently reduced to the following integral equation of the first kind: where , ~' ( 4 ) is known incident wave and Job) is unknown function i.e. current density, satisfying the edge condition in such a form: J~(p)=[d(p)] H(p) . Here H@) is a smooth function on S and d(p) is the distance to the nearest edge point of t l e ring. Because of the axial symmetricity of the ring the two dimensional integral equation (1) can be reduced to an infinite set of one-dimensional equations of the first kind, -112 b -um '(rq) =2nl jm(rp) Gm(rq,rp).rpdrp; m=O,fl,f2, ...,a where a the is inner radius of the ring, b is the outer radius of the ring, rq and rp are r -coordinates of points q and p in polar coordinate system, U ', is Fourier coefficients of incident wave,j, is Fourier coefficients of unknown function, G, is Fourier coefficients of Green function values on the ring. To transform Eq.(2) into a form to solve by means of Chebyshev orthonormal polinomials, a linear transform of interval [a,b] is necessary. It maps the points in the interval [a,b] one-to-one to [-1,1], which is the interval that Chebyshev polynomials