This paper for the first time proposes a simplified rule to estimate effectiveness of the oil damper attached to a building fbr passive control of responses against earthquake or wind. The rule considers the in-series connection of the damper and elastic elements such as the brace member and connection device, and estimates deformation lag and loss caused by such an arrangement. Equivalent linearization using newly defined storage stiffiiess and loss stiffness is proposed. Accuracy of the rule is demonstrated by comparing with many numerical experiments. Dynamic properties and basic responses of the passive control system with the oil damper are explained by using the proposed rule.