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The molecular structure of several high‐density polyethylenes of different molecular weights and vinyl contents was modified without altering their thermoplastic character using an organic peroxide. Chain linking was the main chemical event that occurred during the modification process. Samples of these polymers were crystallized from the melt, generating materials with different morphologies. Two crystallization procedures were followed: slow cooling and quenching. The density and crystallinity of the polymers were found to be slightly dependent on the molecular structures generated by the modification process. Tensile tests were performed at room temperature to evaluate the mechanical behavior of the polymers. The mechanical response of some of the slowly cooled samples changed from brittle to ductile when increasing concentrations of peroxide were added to the formulation. All the quenched samples displayed ductile behavior. The elastic modulus and yield stress were found to increase linearly with the crystallinity of the polymers independently of the molecular structure generated by the modification process. The molecular weight of the modified polymers appears to be the main structural property that influences the draw ratio after break and the ultimate tensile stress of the samples. The draw ratio diminishes, while the ultimate tensile stress increases with the molecular weight of the polymers, irrespective of the evolution of other molecular parameters.