This paper deals with theoretical investigations of the extension of very thin highly elastic filaments as a function of fibrilar diameter. Some specific phenomena are predicted. If the diameter of the fibril is lower than a certain critical value, a nonmonotonous region appears on the stress–strain curve. In this region, a transition from slightly deformed to highly stretched (oriented) states occurs due to a special neck propagating along the fibril. A simple theoretical description of these phenomena is developed in terms of a given general high‐elastic dimensionless potential and two dimensionless parameters which characterize the external force and surface tension. These effects are illustrated by theoretical calculations using neo‐Hookean properties for the highly elasticmaterial.