We investigate scalar problem of diffraction of a plane wave on a system of obstacles consisting of disjoint smooth screens Ωi and volume inhomogeneous bodies Qj . The original boundary value problem leads to a system of weakly singular integral equations on two- and three-dimensional manifolds. We obtain important results on smoothness of the solution to the system of the integral equations in the interior points of the screens, on the equivalence of the integral equations to the original boundary value problem. Finally we prove the invertibility of the integral operator. We propose Galerkin method for numerical solving of the integral equations. We prove the approximation property for the piecewise constant basis functions as well as the statement of Galerkin method convergence.