The deformable fluid actuators available on the market, i.e. pneumatic muscles and pneumatic springs, are designed to mainly exert compressive or tensile forces. This paper deals with a novel fluid deformable actuator, with three membranes, called BiFAc3, whose particular feature is the ability to exert both tensile and compressive forces. The structure of the actuator is based on three cylindrical coaxial nonisotropic membranes connected to two end plates, whose original shape allows the independent supply of the three internal chambers. The first part of the paper deals with the internal structure and the geometry of the actuator, describes the operating principle and presents a prototype. The second part presents a modelling methodology that can be used to design and analyse the actuator in dynamic applications. The mathematical model of the actuator is based on three different levels of complexity which correspond to three consecutive design stages. The model has been experimentally validated: it is a useful tool for the choice of the actuator’s geometrical dimensions, in order to satisfy specific applicative requirements.