In the present work, by using the exact non-linear equations of an incompressible inviscid fluid contained in a prestressed thin elastic tube, the possibility of propagation of a localized travelling wave solution is investigated. Employing the hyperbolic tangent method and considering the long-wave limit, we showed that the lowest-order term in the perturbation expansion is governed by the Korteweg-de Vries equation. The solitary wave type of solution is also given for the second-order terms in the expansion. The correction terms in the speed of propagation are also obtained as a part of the solution of perturbation equations. The applicability of the present model to flow problems in arteries is also discussed. (C) 1998 Elsevier Science Ltd. All rights reserved.