On the other hand, plastics can be very soft but are still considered solid because they have rigidity and do not flow. Solids are elastic when small stresses are applied. They deform but return to their original shape when the stress is removed. When higher stresses are applied some solids break while others exhibit plasticity. Plasticity means that they deform and don't return to the original shape when the stress is removed.
Many substances including metals such as copper have plasticity.
The resistance to flow under plastic deformation is called its viscoplasticity. This is like viscosity except that there is a minimum stress known as the elastic limit below which there is no plasticity. So an arbitrary measure of viscosity or viscoplasticity is not a good way to distinguish solids from liquids. Another way to define the distinction between solid and liquid is to say that, if there is a minimum shear stress required to produce a permanent deformation then it is a solid. This is just a precise way of saying it has some rigidity.