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In this paper we will show a review of the Green-Naghdi thermoelasticity theory. Such model have beautiful foundations which contains since the law of heat conduction proposed byFourier, fundamentals variables such as Helmholtz free energy, entropy, flux of heat and etc. and the constitutive hypothesis. The nature of partial differential equation of parabolic (PDE) type derived from classical thermoelasticity lead us to a mathematical inconsistency well-know as thermal signal speed paradox. We will show how Green-Naghdi model solved those mathematical inconsistency introducing different types of flow and giving us a hyperbolic PDE.

Types of flow in Green-Naghdi Thermoelasticity Theory