Understanding the influence of residual stress fields on fracture behavior remains a critical challenge in computational fracture mechanics. The interaction between evolving cracks and residual stresses often leads to unstable or catastrophic failure, which is difficult to capture using conventional numerical approaches. In this study, we propose a computational framework for fracture analysis in solids with residual stress fields based on the Particle Discretization Scheme Finite Element Method (PDS-FEM). In PDS-FEM, field variables are discretized using conjugate Voronoi and Delaunay tessellations with discontinuous, non-overlapping shape functions, allowing the deformation of the solid continuum to be represented as the translational motion of rigid body particles. Despite this nonstandard discretization, PDS-FEM achieves accuracy comparable to conventional linear finite element methods. Owing to these characteristics, PDS-FEM enables a quantitative evaluation of the release and redistribution of residual stresses during crack propagation, without relying on material-specific assumptions or scale-dependent parameters. Both quasi-static and dynamic fracture processes can be treated within a unified computational framework. Numerical examples are presented for fracture phenomena driven by residual stresses, including desiccation cracking, thermally induced cracking, and fracture of tempered glass. The simulation results demonstrate excellent agreement with experimental observations, capturing crack patterns and fracture processes. To the authors’ knowledge, this study presents the first numerical simulations of dynamic fracture processes governed by residual stress fields. Our results contribute to the development of advanced computational techniques for fracture by providing a versatile computational approach for analyzing fracture processes in materials and structures with residual stress fields.