This chapter is devoted to the application of fractional calculus in mechanics of materials and thermodynamics. The use of fractional calculus in mechanics is related to the definition of fractional-order constitutive equations leading to the class of fractional hereditariness. In this regard, a brief description of the classical rheological models of material hereditariness and a comparison with the fractional elements are reported. It is shown that a rheological hierarchy corresponding to the fractional order stress-strain relation may be defined. Such a model provides a multi-scale mechanical picture of the power-law hereditariness and it leads toward an unique definition of material free energy. The chapter is also devoted to the investigation of the fractional-order Fourier equation. The analysis of the anomalous heat transfer has been conducted with the a multi-scale approach similar to that used in material hereditariness. Thermodynamic consistency of the model has been reported in terms of the irreversible entropy production.