The angular distribution of solute molecules, and the space‐averaged stresses in the fluid, are computed for steady shear flows of solutions of rigid dumbbells. The computation is done by Galerkin's method, with spherical harmonics as the trial functions. The stresses are tabulated for the full range of shear rates,0⩽λhκ⩽∞,and dumbbell width/length ratios,0⩽h⩽38.The stress components become power functions of shear rate when the latter is large. The analogy of Cox and Merz bolds better for small width/length ratios(h≐0)than for large ones.