In the given work some principles of drawing up of mathematical models of transfer and executive mechanisms of independent movement with elastic parts are resulted. In mechanisms with considerable elastic parts the complete cycle of their movement is supposed to be considered as separate periods. In the various periods of movement the elastic parts are represented both as communication, and as source of movement. The questions of drawing up of mathematical models of resulted executive mechanisms of independent movement and definition of inertial parameters of separate mechanisms of variable structure with elastic connections are considered. In the given work the questions of definition of elastic forces of longitudinal deformable connecting-rod of 4-part mechanism are considered, also the equation of movement of flat 2- rocker mechanism in view of weight of elastic connecting-rod is drawn up. The system of the equations describing the movement of 2-rocker mechanism with elastic connecting-rod.