This paper is devoted to the solution of multidimensional integral convolution-type equations on the m-dimensional Euclidian space’s subset with a piecewise boundary. The kernel of the convolution operator is assumed to belong to the \(L_1\)-space, and the right side and the required solution are assumed to belong to the \(L_p\)-space. At the points of the set in question, which are far from the boundary, the solution is sought for with the help of a convolution operator in the entire space or a convolution operator on a torus; near smooth parts of the boundary it is sought for with the help of convolution operators in half-spaces. At the remaining points, the solution is sought for numerically. The paper provides the estimates of arising errors, which prove the method is efficient for large sets with gently sloping boundaries. The work is essentially based on the local method of investigation of the projection method applicability developed by I. B. Symonenko and A. V. Kozak.