The most important pure elastic constitutive laws commonly utilized to model and analyze contact-impact events in the context of multibody mechanical system dynamics are presented in this chapter. Additionally, the fundamental issues related to the generalized contact kinematics, developed under the framework of multibody system dynamics formulation, are briefly described. In this process, the main contact parameters are determined, namely the indentation or pseudo-penetration of the potential contacting points, and the normal contact velocity. Subsequently, the linear Hooke's contact force model and the nonlinear Hertz's law are presented together with a demonstrative example of application. Some other elastic contact force models are also briefly described.