The stress-strain behaviour at ambient temperature has been studied for a set of commercial polyethylenes. High density polyethylenes, HDPE, and linear low density polyethylenes, LLDPE, have been considered. In the first group, the linear structure is slightly modified by random copolymerization with the alpha-olefins, 1-propene, 1-butene and 1-hexene, at a concentration lower than 1% molar. In the second group, the comonomers employed were 1-propene, 1-butene, 1-hexene and 1-octene at a concentration lower than 3% molar. The structural variables, the level of crystallinity, the structure and amount of the interfacial and amorphous regions, and the size of the lamellar crystallites, have been correlated with the chemical structure of the ethylene-alpha-olefin copolymers and with the main characteristics of the deformation, the initial modulus, the yield stress and the ultimate properties, draw ratio and strength at break. The small deformation properties, modulus and yield, depend on the branch content but do not depend on the branch type. Consequently, these parameters were found to depend on the core crystallinity. On the other hand, the draw ratio at break was found to be invariant with the co-unit content and the core crystallinity. The ultimate tensile strength decreases when the mol % branch content increases. The final properties are found to depend on molecular weight.