<p>The Schwarz problem for the classical Cauchy–Riemann system in a flat domain is to determine its solution by the known first component of this solution on the boundary of the domain. In this paper, we consider an analog of this problem for the Moisil–Theodorescu system in a three-dimensional domain bounded by a smooth surface. We propose explicit expressions of the kernel and cokernel of this problem in terms of topological invariants of the domain and the kernel and cokernel of the integral representation of solutions of the Moisil–Theodorescu system that are closely related to the Schwarz problem.</p>