<p>Driven by advancements in functionally graded (FG) materials and their increasing engineering applications, this study explores the influence of material inhomogeneity on the elastoplastic behavior of FG thick-walled pipes subjected to internal pressure, assuming plane strain conditions. The elastic modulus and yield strength are modeled as radially varying power-law functions, while Poisson’s ratio is assumed to be constant, reflecting its minimal variation in typical materials. The novelty of this work lies in providing exact, comprehensive elastoplastic solutions for FG thick-walled pipes, addressing all deformation zones. We analyze the variation patterns of radial and circumferential stresses through their derivatives and investigate the effects of material parameters and wall thickness on stress distributions. Radial stress consistently exhibits compressive and monotonic behavior, while circumferential stress displays three distinct variation patterns that can be controlled by adjusting the gradient index of the elastic modulus and the pipe's geometric dimensions. Exact solutions for stress distributions within the elastic–plastic zone are derived, establishing a clear relationship between internal pressure and the location of the elastoplastic interface. In comparison with homogeneous materials, FG pipes offer the advantage of tailoring stress distributions and the onset of plastic yielding by modifying material properties and wall thickness. These findings provide valuable insights for designing FG pressure vessels that can effectively resist yielding under high circumferential stresses.</p>