As a key element in urban water supply and drainage networks, bell-and-spigot jointed Prestressed Concrete Cylinder Pipes (PCCPs) are required to maintain structural integrity under complex operational conditions. This study presents a detailed three-dimensional finite element model developed in ABAQUS, which incorporates both pipe–soil interaction and bell-and-spigot joint geometry. The model was used to systematically investigate the mechanical responses and failure mechanisms of PCCP under varying internal water pressures and overburden loads. The results indicate that a rapid increase in internal water pressure can critically compromise structural integrity. Specifically, tensile cracking initiates in the mortar coating at an internal pressure of 0.8 MPa. When the pressure exceeds 1.2 MPa, the principal tensile stress in the concrete core surpasses its tensile strength, leading to potential structural failure. Under overburden loading, the mortar coating and bell-and-spigot joint are identified as the most vulnerable components. The ultimate failure load increases with burial depth, and safety thresholds are proposed for different embedment conditions. These findings provide theoretical insights and practical guidance for the safe operation and maintenance of PCCP pipelines.