AbstractA linear lattice model without adjustable parameters provides an accurate description of the magnitude and temperature dependence of the thermal conductivity of Kc of polyethylene crystals parallel (∥) and perpendicular (⟂) to the chain direction. The model shows that heat is transported principally by phonons polarized transverse (T) to the chain direction. Phonons polarized longitudinal (L) to the chain direction contribute about 20% to the heat transport along the chain direction, and negligibly to heat transport perpendicular to the chain direction. Thermal resistance is caused by LTT three‐phonon umklapp scattering in the parallel direction, and by TTT scattering in the perpendicular direction. The calculated values for large crystals are K = 465 W m−1 K−1, K = 0.16 W m−1 K−1 at 300 K, in agreement with experimental estimates and implying an anisotropy ratio of K/K ≈ 3000. The axial thermal conductivity of polyethylene crystals is extremely high and comparable to that of copper. Comparison with experimental data on semicrystalline samples at lower temperature yields a crude value of mean free path for boundary scattering of about 50 nm, agreeing in order of magnitude with the size of crystalline blocks.