Summary: 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 in the used finite strain tensor). The obtained solution is exact since in equations connecting Cauchy stress tensor and Almansi finite strain tensor all nonlinear terms are kept (for accepted medium model the maximum is the fourth power of components of displacement gradient tensor).