Elasticity has meanings in two different fields:
In physics and mechanical engineering, the theory of elasticity describes how a solid object moves and deforms in response to external stress. An alternative meaning of elasticity is a property of an object: it undergoes elastic (as opposed to plastic) deformation in response to stress.
In economics, elasticity is the proportional change in one variable relative to the proportion change in another variable. The concept of elasticity can be used whenever there is a cause and effect relationship. The causal variable is often called the independent variable, while the effected variable is called the dependent variable.
Note: in economics, an inelastic relationship implies that the relationship is still proportional, but with a low constant of proportionality (e.g., price inelasticity). However, in physics, inelastic material (or inelastic collisions) do not obey the theory of elasticity: there is no constant of proportionality. In physics, a material with a high elastic modulus is still technically called elastic.