The dynamical behavior of cyclic macromolecules in a fixed obstacle (FO) environment is very different than the behavior of linear chains in the same topological environment; while the latter relax by a snake-like reptational motion from their chain ends(1) the former can relax only by contour length fluctuations since they are endless.(2) Duke, Obukhov and Rubinstein proposed a scaling model (the DOR model) to interpret the dynamical scaling exponents shown by Monte Carlo simulations of rings in a FO environment.(2) We present a model (blob-spring model) to describe the dynamics of flexible and non-concatenated ring polymer in FO environment based on a theoretical formulation developed for the dynamics of an unentangled fractal polymer.(3) We argue that the perpetual evolution of ring perimeter by the motion of contour segments results in an extra frictional load. Our model predicts self-similar dynamics with scaling exponents for the molecular weight dependence of diffusion coefficient and relaxation times that are in agreement with the scaling model proposed by Obukhov et al.(2).