Extremely dilute solutions of certain high molecular weight polymers are known to exhibit anomalous momentum and heat transfer properties such as drag reduction. In order to study the possible connection between these phenomena and the viscoelasticity of the polymer solutions, a Generalized Convected Maxwell model is used to examine transient shear behavior, propagation of simple shear waves, and elongational flow. Unlike previous investigations where a simple Convected Maxwell equation was used, the more complete generalized model predicts that the effects of polymer additives on transient shear disturbances and simple shear‐wave propagation are negligible. This observation is confirmed by experimental measurements. For elongational flow, however, the generalized model predicts that the viscoelastic effect of the polymer will introduce unusually high levels of stress even at very low polymer concentrations, provided the flow time and stretching rate are sufficiently high. As a result, elongational flow is a simple deformation that may be important in formulating explanations for the unusual behavior that has been observed in dilute solutions.