The potential energy that is associated with objects that can be stretched or compressed is Elastic Potential Energy. This energy is found in springs and rubber bands for example. Potential energy, in general terms is the energy of the objects due its position. This is the ability to perform work due to its position. An object attached to an elastic device (spring for example) and stretched (or compressed) from its equilibrium position will be pulled or pushed gaining the ability fo perform work. This is the elastic potential energy.
