The global automotive industry faces the challenge of increasing engine efficiency, reducing fuel consumption and the size of them gradually. Not only the engine block must reduce its size, but also other components, requiring more compact and flexible designs using materials such as thermoplastic elastomers. These kinds of materials are used due to their characteristics, such as ability of deformation, durability, recyclability, and its cost/weight ratio. They are able to hold large deformations and they have very good damping characteristics, making them suitable for use in energy dissipation. Characterization of the dynamic mechanical properties of these materials is essential to make a correct analysis and modeling of the behavior of components. Although the constitutive models of these materials are complex due to high deformability, quasi-incompressibility, softening, and time dependent effects, typically, these materials have a mechanical behavior which can be represented by a phenomenological hyperelastic model. While it is easy to fit a model of elastic behavior, set a model for a hyperelastic material is a very complex task, so in practice simplified models are used. This paper proposes a comprehensive comparison of six hyperelastic models to simulate the behavior of Santoprene 101-73 material manufactured by ExxonMobil. The ability of these models to reproduce different types of loading conditions is analyzed through uniaxial tensile data obtained experimentally. The parameters of each of the hyperelastic models are determined by a least-squares fit and then a classification of these six models is established, highlighting those that are most suitable for characterizing the material.