A method is introduced for extracting tensorial stress measures from rigid-body-spring networks with random geometry. Stress analysis of a uniformly stretched material indicates that rigid-body-spring networks can be made elastically homogeneous provided two basic conditions are met: 1) network geometry is defined by a Voronoi diagram, and 2) the network degrees of freedom are defined at the Voronoi cell nuclei. For more general loadings, accuracy of the stress retrieval algorithm is demonstrated through comparisons with finite element analysis results, where the finite element mesh is based on the corresponding Delaunay triangulation of the domain.