The effect of shear on polymer crystallization kinetics has been studied for three materials at several shear rates and degrees of supercooling. Two poly(ethylene oxide) samples, with molecular weights of 72, 200 and 12, 600, and a poly(e‐caprolactone) material, with a molecular weight of 9, 400, were investigated. The apparatus used was a concentric cylinder viscometer, which also functions as a dilatometer, capable of detecting very small volume changes on crystallization. The shear‐rate range of the experiments was 0 to 60 sec−1. Avrami kinetics were used to describe the transformation process and the exponent was found to increase from the quiescent value of 3 to a value greater than 5 with increasing shear rate for all materials studied. The acceleration in the transformation process was associated with a reduction in induction time. The value of induction time at high shear rates did not significantly decrease with increasing shear rate, indicating a saturation effect with shear. This was most pronounced in the low molecular weight samples. The value of induction time for the high molecular weight poly(ethylene oxide) sample, under identical experimental conditions, was substantially less than that of the low molecular weight material in all cases. Nuclei formation measurements were made for the crystallizing melt in a separate instrument. Nuclei formation under shear was very different from quiescent behavior and increased substantially with increasing shear rate. These experimental observations lead to the conclusion that accelerated crystallization is due to increased molecular chain extension and orientation under shear. This orientation greatly enhances the nucleation process, which is thought to be the rate controlling step in the crystalline transformation. This enhancement results in shorter induction times and more rapid crystallization.