The paper is devoted to development of models for description of waves in tubes with elastic walls in the case when a tube is filled by liquid. It is also devoted to development of numerical methods for these models and analysis of solutions with reversible shock structures. Membrane model and plate model are used for tube. Numerical methods for solving equations are developed. The ability of stabilization of numerical method by the aid of inclusion of additional term with higher-order derivatives is analyzed. Riemann problem is solved.

tube, elasticity, fluid, dispersion, nonlinearity, shock structure, numerical method, Riemann problem

Mathematical problems and theory of numerical methods