The paper presents an adaptive section discretization scheme for the inelastic response analysis of structural members with cross sections that can be decomposed into rectangular and circular subdomains. Each subdomain can consist of a different material. As long as the largest strain in a subdomain does not exceed the specified trigger strain values, the subdomain contribution to the section response is determined by the numerically exact cubature rule for the subdomain. Once the largest strain reaches the trigger value for a subdomain, it is discretized with a fiber mesh and the numerical evaluation of its contribution to the section response is determined with the midpoint integration rule. The fiber mesh with the midpoint integration rule remains in effect for the activated subdomain until the end of the response history. The paper applies the adaptive discretization scheme to the thin-walled sections common in metallic structures and investigates the effect of different trigger strain values on the accuracy and computational efficiency of the inelastic response analysis of wide-flange steel sections and multistory steel frames under static and dynamic excitations.