The paper presents a methodology to model 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 level set function $\varphi$ represents the location of holes and inclusions, and it is also used to develop local enrichment functions for material interfaces. The X-FEM enriches the finite-element approximation by additional functions through the partition of unity concept. Numerical examples in two-dimensional linear elastostatics demonstrate the accuracy and potential of the method. The technique is shown to achieve optimal convergence rates and provide accurate results for problems involving holes and inclusions. The study highlights the simplicity and versatility of the approach, making it a promising tool for modeling interfacial phenomena in solid and fluid mechanics.The paper presents a methodology to model 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 level set function $\varphi$ represents the location of holes and inclusions, and it is also used to develop local enrichment functions for material interfaces. The X-FEM enriches the finite-element approximation by additional functions through the partition of unity concept. Numerical examples in two-dimensional linear elastostatics demonstrate the accuracy and potential of the method. The technique is shown to achieve optimal convergence rates and provide accurate results for problems involving holes and inclusions. The study highlights the simplicity and versatility of the approach, making it a promising tool for modeling interfacial phenomena in solid and fluid mechanics.