A simple procedure, based on Love’s approximate theory [TheMathematicalTheoryofElasticity(Cambridge U. P., Cambridge, England, 1927), 4th ed.] for wave propagation in a bar, is proposed in order to consider dispersive effects in wave propagation in a thin‐walled, fluid‐filled, elastomer tube. It is assumed that the perturbation from steady flow in the tube is small enough that a linearized theory is valid, and that the elastic modulus of the tube is small compared with the bulk modulus of the fluid so that compressibility of the fluid can be neglected. The flexural rigidity of the tube wall, the inertia of the tube wall, and the radial inertia of the fluid are taken into account, and an approximate expression for the dispersion relation for the fundamental mode is obtained. In order to investigate the dispersive effects, resulting from inclusion of the inertia and flexural rigidity of the tube wall and the radial inertia of the fluid in the model, an initial value problem is considered in detail. The fast Fourier transform is used to obtain numerical solutions for small and intermediate times. Numerical results are presented in graphical form.