Viscous deformation is the deformation in which the deformation varies linearly with time. The material does not come back to its original position. Examples of viscous deformation are honey, wax, etc.
Elastic Deformation is the deformation in which the material returns to its original shape after the stress is removed. In elastic deformation, the deformation is proportional to the stress. Eg. Metals.
Viscoelastic deformation.
Certain materials exhibit both viscous and elastic deformation. In these materials, some deformation is elastic while some deformation is viscous. Examples are rubber, plastics, etc. Wood is also a viscoelastic material.
Applications
Viscoelastic materials are used in applications where vibration damping is required. Viscoelastic materials are also used where impact and shock absorption are required, such as the bumper of a car.