Viscoelastic materials are those for which the relationship between stress and strain depends on time or, in the frequency domain, on frequency. Viscoelastic materials have properties that depend on strain rate.
Anelastic solids represent a subset of viscoelastic materials: they have a unique equilibrium configuration and ultimately recover fully after removal of a transient load. After being squeezed, they return to their original shape, given enough time. Transient strain is recoverable after the load or deformation is removed. The time scale for recovery may be very short, or it may be so long as to exceed the observer's patience or even lifetime.
Elastic solids exhibit no dependence on time. The elastic stiffness or compliance is independent of time after force is applied. The stiffness is independent of frequency of oscillatory deformation.
Elastic, anelastic, or viscoelastic materials can be linear or nonlinear.