Abstract <p>The quasi-static deformation of a liquid-filled cylindrical shell under a radially distributed moving load is considered. The two approaches employed differ in how the initial deformed state of the shell due to the liquid’s hydrostatic pressure is taken into account. The action of the mobile load is analyzed in a quasi-static approximation. Expressions describing the load’s critical velocity are obtained in each approach. Closed analytical formulas are derived for the smaller value. Numerical examples illustrate the results.</p>