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This paper studies the mechanical behavior of high-density polyethylene (HDPE), from which the pipes used for water transport in water supply networks are manufactured. The study was generated by the practical problem of replacing and modernizing a water network of a city with 300,000 inhabitants. Of the numerous problems that have arisen and been solved by the group of researchers, only those referring to the mechanical behavior of the materials used for pipes are presented. HDPE, which is a thermoplastic material, is suitable for manufacturing the pipes used in water supply networks, having many advantages. Data on the mechanical properties of the material of which the pipe and elbow are made is obtained experimentally. The work involved the main steps required to design a water network, but the subject is not exhausted. The stresses in the polyethylene pipe are determined in two cases: buried in the ground and supported in a concrete massif. Thus, by calculation, the advantage offered by the second solution is justified. The crack of the pipes manufactured from HDPE is studied, taking into account the classical model used in the cracking process. A simulation of pipes and elbows cracking was made. The results obtained via MEF are useful for the users of the networks.