In the present work, by employing the approximate nonlinear equations of an incompressible inviscid fluid contained in a prestressed thin elastic tube, the propagation of a localized travelling wave solution is examined. Employing the hyperbolic tangent method and considering the longwave limit, we showed that the lowest order term in the perturbation expansion is governed by the Korteweg-de Vries equation of which the solution may be expressed as a solitary wave. It is also shown that the second order terms in the expansion can be described by a solitary wave. The correction terms in the speed of propagation are also obtained as a part of the solution of the perturbation expansion. The applicability of the present model to flow problems in arteries:is also discussed. (C) 1999 Elsevier Science Ltd. All rights reserved.