Using thermal neutron scattering kernels suggested for crystalline and noncrystalline polyethylene (PE) various thermal neutron transport processes, such as pulsed neutron, temperature-dependent diffusion length, and temperature- and absorption-dependent steady-state spectra have been studied. The calculated values of the fundamental decay mode in pulsed neutron problems in crystalline PE at 293 K agree with the experimental results of Sjöstrand et al. and Graham and Carpenter for a large buckling range B2 = 0 to ∼ 1.5 cm-2. The time-dependent neutron density for crystalline and amorphous PE is essentially the same and agrees well with the experimental results of Fullwood et al. The propagation of a neutron pulse is therefore independent of the degree of crystallinity of PE. The thermalization time for B2 <1.0 cm-2 is almost constant at ≃12.5 µs. The calculated values of the temperature-dependent diffusion length in crystalline PE in the temperature range from 293 to 400 K agree well with the experimental results of Esch. The computed diffusion lengths in amorphous PE are the same as those in crystalline PE. The space-dependent spectra for different absorptions have also been reported. Steady-state spectra calculations for crystalline PE at 293 K for natural absorption and for absorptions corresponding to 5.74 and 10.45 b/H atom agree well with the experimental results of Young et al. A somewhat detailed study at lower temperatures down to 4 K shows that the effective temperatures of neutron spectra are the same as those at 21K and correspond to 46 K. Thus PE can be a good source of cold neutrons down to 21K, and it is unprofitable to cool it below this temperature to obtain a still larger flux of cold neutrons. The above studies have also been performed on amorphous PE and yield almost the same results as those obtained in crystalline PE. Thus the transport of thermal neutrons is more or less independent of the degree of crystallinity of PE.