Abstract In this work, we studied the propagation of solitary waves in an incompressible inviscid fluid contained in a thick walled and prestressed elastic tube. In order to include the geometrical and structural dispersion into analysis, the wall's inertial and shear effects are taken into account in determining the inner area-inner pressure relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is investigated. Contrary to the result of thin tube approximation, it is shown that in the present approach it is possible to have solitary waves even for the Mooney-Rivlin material. Due to dependence of the coefficients of the governing Korteweg-de Vries equation on initial deformation and the geometrical characteristics of the tube material, the wave profile changes with these characteristics. These variations are calculated numerically for a class of elastic materials and the effects of initial deformation and the thickness ratio on the propagation characteristics are discussed.