Energy stored in a stretched elastic band or spring is called elastic potential energy. The amount of energy stored is equal to the energy required to stretch the elastic band or spring, which is dependent upon the spring constant (denoted by the letter 'k') and the distance stretched, x. Using Hooke's law, this energy can be calculated as:
Elastic potential energy = `1/2 kx^2`
The elastic potential energy is also generated when the elastic spring or band is compressed. This energy is beneficially used in a number of applications. Think about how the dart gun works. We compress the spring inside the dart gun with the dart and it is the elastic potential energy of the compressed spring that propels the dart forwards. Another example of application of elastic potential energy is the bungee cord, which is used for bungee jumping.
Hope this helps.