With advancements in seismic isolation and damping technology, high-damping rubber (HDR) bearings are now widely used. However, significant gaps remain in HDR-analysis model research, with few studies integrating multiple factors, the Mullins effect, and stiffness hardening for more accurate practical predictions. This study classifies the effective behavior of HDR and examines the stress–strain relationships of different behavioral types using more appropriate equations. Mathematical models were established based on pseudo-elasticity theory, which is an extension of continuum mechanics. Subsequently, parameter functions were developed through parameter determination tests and regression analysis, leading to the completion of the pseudo-elastic model for HDR. Finally, the model’s effectiveness was validated through validation tests. This study finds that behavior classification effectively examines phenomenological-based HDR stress–strain relationships, as distinct behavioral patterns are not adequately captured by a single approach. Incorporating tests to functionalize material parameters complements theoretical models. Additionally, accurately explaining HDR behavior requires considering the Mullins effect and stiffness hardening, influenced by the coupled effects of temperature, strain amplitude, and compressive stress. Consequently, this HDR pseudo-elastic model offers a comprehensive explanation of HDR behavior, including the Mullins effect and stiffness hardening, under various influencing factors based on clear mechanical principles and explicit computational procedures.