  The paper is devoted to analysis of different models that describe waves in
fluid-filled and gas-filled elastic tubes and development of methods of
calculation and numerical analysis of solutions with solitary waves and kinks
for these models. Membrane model and plate model are used for tube. Two types
of solitary waves are found. One-parametric families are stable and may be used
as shock structures. Null-parametric solitary waves are unstable. The process
of split of such solitary waves is investigated. It may lead to appearance of
solutions with kinks. Kink solutions are null-parametric and stable. General
theory of reversible shocks is used for analysis of numerical solutions.
