This paper presents a methodology for modeling arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries using the extended finite-element method (X-FEM) combined with the level set method. The X-FEM enriches the finite-element approximation by additional functions through the concept of partition of unity, while the level set method is used to represent the location of holes and material interfaces. The level set function is also used to develop the local enrichment for material interfaces. Numerical examples in two-dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique. The method is shown to be effective in modeling voids and inclusions, with the level set function providing a convenient and flexible way to represent internal boundaries. The approach is validated through convergence studies and comparisons with exact solutions, demonstrating its accuracy and efficiency. The results indicate that the X-FEM with level set enrichment provides a powerful and accurate numerical technique for modeling voids and inclusions without meshing the internal boundaries. The method is simple and versatile, with potential applications in solid and fluid mechanics.This paper presents a methodology for modeling arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries using the extended finite-element method (X-FEM) combined with the level set method. The X-FEM enriches the finite-element approximation by additional functions through the concept of partition of unity, while the level set method is used to represent the location of holes and material interfaces. The level set function is also used to develop the local enrichment for material interfaces. Numerical examples in two-dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique. The method is shown to be effective in modeling voids and inclusions, with the level set function providing a convenient and flexible way to represent internal boundaries. The approach is validated through convergence studies and comparisons with exact solutions, demonstrating its accuracy and efficiency. The results indicate that the X-FEM with level set enrichment provides a powerful and accurate numerical technique for modeling voids and inclusions without meshing the internal boundaries. The method is simple and versatile, with potential applications in solid and fluid mechanics.