Fractional Viscoelasticity is referred to materials, whose constitutive law involves fractional derivatives of order beta is an element of R such that 0 <= beta <= 1. In this paper, two mechanical models with stress-strain relation exactly restituting fractional operators, respectively, in ranges 0 <= beta <= 1/2 and 1/2 <= beta <= 1 are presented. It is shown that, in the former case, the mechanical model is described by an ideal indefinite massless viscous fluid resting on a bed of independent springs (Winkler model), while, in the latter case it is a shear-type indefinite cantilever resting on a bed of independent viscous dashpots. The law of variation of all mechanical characteristics is of power-law type, strictly related to the order of the fractional derivative. Because the critical value 1/2 separates two different behaviors with different mechanical models, we propose to distinguish such different behavior as elasto-viscous case with 0 <= beta <= 1/2 and visco-elastic case for 1/2 <= beta <= 1. The motivations for this different definitions as well as the comparison with other existing mechanical models available in the literature are presented in the paper. (C) 2012 The Society of Rheology. [http://dx.doi.org/10.1122/1.4717492]