Abstract—Modern vacuum technology requires the creation of robots that do not fill the working area with micro-particles of wear and friction between the elements. The mechanisms in which a flexible elastic thin-walled element with any shape of the axis is used as a working element are considered. The moving of an element is carried out at submission of pressure in a cavity of an element. The given task is nonlinear and are reduced to the second regional task Koshee. For the decision the method of discrete continuation on parameter in a combination to a method multisegment shooting is used. The technique allows to pick up under the given law of moving geometrical parameters of a flexible element.