AbstractMotivated by the effectiveness of inerters to control the displacements of flexible structures in association with their known property to eliminate the participation of higher modes, this paper revisits the seismic response analysis of the classical two‐degree‐of‐freedom isolated structure with supplemental rotational inertia in its isolation system. The paper shows that for the “critical” amount of rotational inertia which eliminates the participation of the second mode, the effect of this elimination is marginal on the structural response since the participation of the second mode is invariably small even when isolation systems without inerters are used. Our study, upon showing that the reaction force at the support of the inerter is appreciable, proceeds with a non‐linear response analysis that implements a state‐space formulation which accounts for the bilinear behavior of practical isolation system (single concave sliding bearings or lead‐rubber bearings) in association with the compliance of the support of the inerter. Our study concludes that supplemental rotational inertia aggravates the displacement and acceleration response of the superstructure and as a result, for larger isolation periods () the use of inerters in isolation systems is not recommended.