In this paper is given an over view of histor y of creation and development of geometrical mathematical models and use of pneumatic artificial muscles (PAM) and bellows. PAMs and bellows as pneumatic actuators are made of flexible membrane which can inflate. Displacement of these membranate elements depends on inner pressure. Direction of the displacement coincide with elements symmetry axis. Process of displacement involve shell form change. Reviewing actuators can be divided into two types: push-type and pull-type. The direction of displacement depends on length and diameter ration of element. PAMs are related to the pull-type actuators, bellows are related to the push-type. Distinguished tendencies and perspectives of developing pneumatic actuators are based on force membranate elements because of their advantages such as small weight, smoothness on low velocities and high strength. True to date exist big amount of different constructive designs of PAMs and bellows. Review contains such designs as braided, pleated and other designs of PAMs. In this paper are given main and often used approaches of creation static geometrical mathematical models of PAMs and bellows. Suggested mathematical models connect such parameters of PAMs and bellows as developed force, element axial length change, inner pressure change, diameter and material characteristics. For PAMs and bellows control is required to control its length or developed force. There are shown some applications of force membranate elements in different fields, such as biorobotics, medical and industrial applications. In conclusion are given possible approaches to improve discussed geometrical mathematical models of PAMs and bellows.