We present a strain sensor in which a multimode fiber is used as a sensitive element. High sensitivity to dynamic strains is achieved by means of vectorial wave mixing in a photorefractive CdTe:V crystal. It was found that the largest source of noise in our sensor is related to the instability of the polarization state of speckles emerging from the fiber. This noise is significantly diminished in fiber with a core of large diameter (550 microm).