The object of research is the Mixed Mode Stress Intensity Factor (MMSIF) of a two-dimensional (2D) plate. With the emergence of modern technologies and advanced innovations which contribute to the development and improvement of the design, implementation and management of construction projects, it has become easier. However, it is very difficult to manufacture components free from unavoidable defects, such as cracks, which lead to material deterioration and ultimately shorten its service life. Based on the process of local enrichment region using partition of unity concept, the extended finite element method (XFEM) has overcome the limitations of the standard FEM method in terms of modeling and numerical simulation of discontinuities (cracks) while gaining its general advantages. This makes XFEM a powerful and widely used digital tool in recent years. One of the most frequently raised problems in the discontinuities field (cracks) is the phenomenon of juxtaposition of multiple cracks in a cracked isotropic plate, which must be studied to determine the extent of its effect on the crack stress intensity factor in order to obtain higher safety reliability. On this basis, an improved object-oriented programming (OOP) with extended finite elements was used because of its great importance and well-known benefits. In this paper, the MMSIF of a 2D plate is determined to show the effect of the out-of-phase orientation of the angle, as well as the effect of the juxtaposition of two inclined cracks. As a result of the research, it is shown that, the convergence between the results obtained in this study with those reported in the literature, and to theoretical values is remarkable, and their close agreement was noted. In the future, based on the object-oriented approach characteristics represented by flexibility, scalability, and modularity, which were explained in this research, this proposed approach can be enriched to include heterogeneous materials modeling, whether linear or nonlinear, crack propagation in dynamics, in addition to Complex 3D industrial problems.