PDS-FEM (Particle Discretization Scheme Finite Element Method) is one of the fracture analysis methods using the conjugate geometries for the discretization of field variables. Since PDS-FEM uses the discontinuous and non-overlapping shape functions, it can express the deformation of the solid continuum as the translational motion of the rigid body particles. This particle description enables the easy treatment of the discontinuous field due to fracture. Another merit of PDS-FEM is that this method can analyze the deformation of the solid continuum with the same accuracy as the conventional FEM with linear first-order element. Owing to these characteristics of PDS-FEM, we have succeeded in the world’s first simulation of fracture in residual stress field. In our presentation, taking desiccation crack and fracture of tempered glass for example, we present the results of PDS-FEM analysis of quasi-static crack propagation and dynamic crack propagation in residual stress field. The desiccation crack is the coupled problem of moisture diffusion and fracture; we perform weak coupling analysis of diffusion and fracture. On the other hand, since the residual stress of tempered glass is given in advance during manufacturing process, the cracks in tempered glass dynamically propagate without any persistent external loading. This dynamic crack propagation process is strongly affected by the intensity of residual stress. Our numerical results perfectly coincide with the experimental results.