Relaxation spectra in polydisperse polymers were calculated by viscoelastic functions of stress relaxation following sudden straining. Inversion of these function provides an accurate way to estimate the molecular weight distribution of viscoelastic poymers. This theoretical treatment of the relationship between relaxation spectrum and molecular weight distribution is useful for determination of molecular weight distribution of insoluble or otherwise intractable polymers. The molecular weight distributions of nylon 6, polyacrylonitrile, undrawn PET and drawn PET filament fibers were obtained from the theoretical relationship between the relaxation spectra and the molecular weight distributions. We will describe the development of the molecular viscoelastic theory of polymers, and show the possibility of using the theory to correlate the molecular weight distribution and the relaxation spectrum from stress relaxation curves.