In pipes made of HDPE used in city water supply networks, a specific type of failure is commonly noted, called the parrot’s beak failure. It requires expensive intervention. The prediction and study of the development of this defect, therefore, requires thorough research. In this work, the finite element method is used to study the mechanism of the occurrence and development of this defect. Two examples of the calculation for the concrete case of some tubes used in a water supply network are presented. This study is important for the designers of such networks, to predict and prevent the occurrence of this defect that can lead to unwanted network downtime and high repair costs.