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An analytical solution of a problem on planar deformation of isotropic incompressible nonlinear-elastic (rubber-like) media with a cylindrical cavity is constructed in quasi-static approximation. A contour of the cavity is a smooth symmetrical curve. The special kind of follower load provides purely radial movement of material. Mass forces are neglected. A physical model of medium is given by elastic potential, which is analogous of Mooney-Rivlin strain energy potential (with a difference indoi:10.17516/1997-1397-2014-7-3-352-355 fatcat:zy4uptjeejdphijzzmyd6w4blu