The magnitude of residual displacement is indicative of the re-centering capacity of the isolation layer and serves as a key indicator for evaluating the operational functionality of the primary structural building elements following an earthquake. Post-earthquake investigations have demonstrated that isolation bearings frequently exhibit residual displacements, resulting in incomplete re-centering of the isolation layer. To reveal the mechanism of residual displacement formation in the isolation layer, a free vibration decay dynamic model was established. This model was based on the Coulomb friction single-degree-of-freedom system and the bilinear hysteresis characteristics of the isolation layer. A simplified calculation formula for the maximum residual displacement was proposed and validated through numerical simulation, providing theoretical support for rationally assessing the re-centering capability of the isolation layer. The findings suggest that the distribution of residual displacements in the isolation layer is characterized by significant discreteness, while its maximum value is quantifiable. The influencing factors include the plastic yield force Q_d, initial stiffness k₀, post-yield stiffness k, and damping ratio ξ. The simplified formula offers practical guidance for the design of isolation engineering.