Krigbaum's modulus theory and its application to polyethylene which was irradiated with γ-rays are discussed in this article. The results indicate that an amorphous chain in a crystalline polymer varies from an inverse Langevin chain to a Gaussian chain with increasing temperature. Krigbaum's parameter Nn(t), the number of statistical segments present in an amorphous chain when its two ends have just deposited themselves on the surface of a growing crystallite, did not depend on the degree of degradation in a sample. By applying Krigbaum's modulus theory to a degraded sample, it was found that the ratio of the theoretical initial Young's modulus for a degraded sample to that for an undegraded sample, E0(t)/E0(0), increased with the degree of degradation in the sample. It seems to be caused by the greater increase of the degree of crystallinity in a degraded sample with such an increase being expected on the basis of the assumption that, after the amorphous regions in a sample degrade, some of the remaining unsevered amorphous chains can crystallize more readily.