AbstractA simple model is introduced to investigate the stability of a sedimenting entanglement. The sedimenting entanglement is represented by a sedimenting sieve. Solvent can pass through it, but single‐chain molecules that flow into it become entangled and their flow decreases or, if permanent entanglements form, ceases entirely. With this model we are able to find the conditions under which the mass of a sedimenting entanglement remains constant, grows or decays to a stable value, grows beyond limit, or decays to the mass of a single chain. The theory is applied to the sedimentation of small concentrations of large chain molecules in solutions of small chain molecules in solutions of small chain molecules for the case in which the entanglements are long‐lived. Equations are derived which, (1) give the stable entanglement mass as a function of rotor speed and concentration and, (2) for a given concentration predict the rotor speed at which the entanglement mass grows without limit. Numerical results for small concentrations of T2 DNA sedimenting in solutions of T7 DNA are presented.