Axial strain on an optical fiber can be determined by monitoring the phase shift of a variety of optical fiber sensors. The exact analytical solutions for optical fields that propagate in a circular core optical fiber are used here to determine the phase shifts that occur for TE and TM modes due to axial strain. Whenever an optical fiber is stressed, the optical path length, the index of refraction, and the propagation constant of each fiber mode change. In consequence, the modal phase term βz of the fields is shifted by an amount ΔΦ. In certain cases, it is desirable to control the phase sensitivity to make fibers that are either more or less sensitive to strain. We show that it can be accomplished by choosing appropriate fiber parameters.