Stress–relaxation behavior of polyurethane elastomers based on two hydroxyl-terminated polyesters: poly(ethylene adipate) and poly(ethylene maleate) was studied. In addition, a polyester-diol consisting of poly(ethylene adipate) and oligo(ethylene terephthalate) blocks, a number of low-molecular-weight diols as chain extenders, and 4,4′-diphenylmethane diisocyanate (MDI) were determined. The elastomers were crosslinked by an excess of MDI and had stiff segments of differing chemical structure and length. Stress–relaxation properties of the elastomers conformed with the three-component Maxwell model, with negligibly small contribution from the fastest relaxation process. The influence of crosslinking density, chemical structure, and stiff segment content on the relative relaxation speed and the parameters of the slow and fast relaxation processes, was examined. The elucidation of the results was based on the morphological models of segmented polyurethanes.