Elasticity is the property of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. So, usual liqids do not have elesticity. But there are some of them which do. Such liquids demonstrates both viscous and elastic behaviour. For example, non-Newtonian liquids (see https://en.wikipedia.org/wiki/Constant_viscosity_elastic_fluid or https://en.wikipedia.org/wiki/Viscoelasticity).
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