Abstract: Stress softening, known as Mullins effect, occurs in rubber-like materials during the first and subsequent deformations. The stress-strain hysteresis loops induced by the Mullins effect will change as the strain rate varies. First, classical elastic potential usually does not consider dissipation, and cannot theoretically explain why the material exhibits stress softening after a loading history. Second, when considering the effects of strain rate, traditional methods often introduce it as a fixed parameter into the equation, which greatly increases the limitations of the model. Third, most of models only consider a single deformation mode, for example, uniaxial tension. whereas real materials may also be subjected to more complex deformation modes such as equi-biaxial tension and plane strain tension. A unified elastic potential is proposed to simulate stress-strain relationship with the Mullins effect in different strain rate. First, constructing evolution equation of dissipation by researching stress-strain relationship in loading-unloading process. Second, proposing shape functions of three benchmark tests by introducing dissipation and strain rate into the characteristic parameters. Third, combined with shape function and three invariants, a unified potential is proposed by using Hermite interpolation method. The results show that the stress-strain relationships under three benchmark experiments can be derived by using a unified elastic potential, and the rate-dependent stress-strain experimental data can be accurately matched and reasonably predicted. All the parameters presented in this article can be determined by explicit methods, thus can significantly reducing computational costs. This work provides essential data and design guidance for the engineering design and practical application of rubber-like materials.