Energy minimizing contours or snakes are tools for delineating objects of interest in an image. Snakes are defined discretely or in continuous form with continuous snakes having advantages over discrete snakes. A continuous snake called B-snake has been previously defined using B-spline curves. In this paper, a continuous snake called R-snake is introduced that is based on rational Gaussian (RaG) curves and has advantages over B-snakes. Not only the stiffness of an R-snake can be varied continuously to delineate an object from coarse to fine, the stiffness of different parts of an R-snake can be adjusted to recover a shape with smooth as well as detailed parts. The formulation of R-snakes is presented and experimental results delineating various objects in synthetic and real images are presented and discussed.