<p>This paper presents a comprehensive examination of residual stresses in pipeline branches, highlighting their critical role in the structural integrity of pipelines. It is a well-documented fact that branches experience the highest stress levels within pipeline systems. In this study, we introduce the novel concept of critical internal pressure, denoted as pres, which signifies the threshold at which the first residual stresses emerge. Our analysis focuses on the stress state when the internal pressure p meets or exceeds pres. We investigated two significant phenomena associated with residual stresses. First, we analyzed the timing of their formation: Do these stresses manifest abruptly, or do they develop gradually over time? Second, we explored the evolution of residual stresses post-formation in circumstances where p is greater than or equal to pres, utilizing both quasi-static and cyclic pressure applications. The findings presented here provide valuable insights, enriching the understanding of the unique behavior of residual and total stresses in pipeline branches. Ultimately, our conclusions elucidate the complexities of stress states in these critical structural components, underscoring the importance of considering residual stresses in pipeline design and assessment.</p>