This paper considers various experimental designs on the Atlas facility to study the physics of liners and determine the optimum conditions of their stable motion. In one of the versions, in comparison with the Liner Demonstration series of experiments, in which unstable liner motion was observed, it is proposed to reduce the initial liner radius without changing its mass, which, according to twodimensional calculations, should to lead to more stable motion of the liner with unchanged velocity. It is also proposed to perform an experiment in which periodic perturbations at a certain wavelength are created on the outer surface of the liner with a simultaneous increase in its thickness. According to calculations, the growth of chaotic perturbations is stabilized in this case with the preservation of the liner velocity.