A mathematical model for large amplitude wave propagation in a thin walled distensible tube is developed. The tube wall is considered as a membranic shell made of an incompressible, non-linear viscoelastic material with cylindrical orthotropy. The fluid is regarded as incompressible and inviscid and the flow is quasi-one-dimensional. The case of a pressure step applied at one end of a uniform straight tube is solved as an example. The system of partial differential equations, describing the motions of the fluid and the wall, are integrated numerically by using a two-step explicit scheme. Flow and deformation variables as well as the wave velocity are determined in time and space.