Flexibility is a measurable range of motion in one specific direction. To increase the flexibility of a tissue, we must apply a force pulling the tissue in an isolated range of motion until the stress causes a permanent deformation of the tissue, where it will not return to its original state. However, over years and a lifetime, we cause micro trauma to our tissue from activity. The tissue heals, but only after scar tissue has formed.
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In healing, the scar tissue mends the wound together by pulling and shortening the tissue.
Many people, in conventional understanding of physical culture, have made the assumption that stretching after activity can prevent the muscle from healing at a shorter length. However, should the stretching manage to prevent shortening (which is debatable), the connective tissues will stiffen regardless. Tendons and ligaments are composed of collagen (lending tensile strength) and elastin (lending elasticity, obviously).
As we age, our tissues endure an irreversible process of increasing collagen and decreasing elastin.
Elasticity is a material's ability to return to its original state following deformation after removal of the deforming load. To increase the elasticity of a tissue, we must apply a load to the tissue in a range of motion, then remove the load, after the initial stiffness ceases (discomfort, not pain) and before the tissue is permanently deformed so that the tissue returns to its original state. This stress increases the capacity for storage of elastic energy.