Lead rubber bearings (LRBs) are a type of isolation bearing that have a combination of rubber and lead as the main components. These bearings are widely used in bridges, buildings, and other important structures due to their high load‐carrying capacity and excellent energy dissipation capability. However, the behavior of LRBs is complex and nonlinear, making it difficult to predict their behavior and performance under different loading conditions. The objective of this research is to develop a comprehensive analytical model of LRBs that can accurately predict their behavior under low to large levels of strain. The proposed model considers nonlinearity, hysteresis, stiffness, damping, and rate‐dependent behavior of LRBs. The model is also able to consider the effect of temperature on the rubber and lead components of the bearing. The developed model is validated using experimental results and is shown to provide accurate predictions of the LRB response under different strain levels. The accuracy of the developed LRB model is also validated using shake table test results of an LRB‐isolated bridge under low and large strain. This research provides a valuable tool for engineers and designers to predict the behavior and performance of LRBs and optimize their design.