In strong flows, such as turbulence, it is suggested that randomly coiled macromolecules might become nearly fully extended. To investigate this extended state, four models are considered which show the importance of the inextensibility of the polymer chain and the variation of the friction coefficient with the extension. The rheological consequences of these processes are then explored in an appropriately modified dumb‐bell model. A dilute polymer solution is predicted to have a high extensional viscosity but a low shear viscosity, a stress hysteresis, and a slow stress relaxation. The action of the novel rheology is shown in two simple flows. Finally, speculations are made on the possible way dilute polymer solutions can modify turbulence.