AbstractCyclic (1 → 4)‐α‐D‐glucan chains with or without excluded volume have been collected from a huge number (about 107) of linear amylosic chains generated by the Monte Carlo method with a conformational energy map for maltose, and their mean‐square radii of gyration 〈S2〉 and translational diffusion coefficients D (based on the Kirkwood formula) have been computed as functions of x (the number of glucose residues in a range from 7 to 300) and the excluded‐volume strength represented by the effective hard‐core radius. Both 〈S2〉/x and D in the unperturbed state weakly oscillate for x < 30 and the helical nature of amylose appears more pronouncedly in cyclic chains than in linear chains. As x increases, these properties approach the values expected for Gaussian rings. Though excluded‐volume effects on them are always larger in cycloamylose than in the corresponding linear amylose, the ratios of 〈S2〉 and the hydrodynamic radius of the former to the respective properties of the latter in good solvents can be slightly lower than or comparable to the (asymptotic) Gaussian‐chain values when x is not sufficiently large. An interpolation expression is constructed for the relation between the gyration‐radius expansion factors for linear and cyclic chains from the present Monte Carlo data and the early proposed asymptotic relation with the aid of the first‐order perturbation theories. © 2002 Wiley Periodicals, Inc. Biopolymers 64: 72–79, 2002