BACKGROUND: Mechanical forces at the micro-scale level have been recognized as an important factor determining various biological functions. The study of cell or tissue mechanics is critical to understand problems in physiology and disease development. OBJECTIVE: The complexity of computational models and efforts made for their development in the past required significant robustness and different approaches in the modeling process. METHOD: For the purpose of modeling process simplifications, the smeared mechanics concept was introduced by M. Kojic as a general concept for modeling the deformation of composite continua. A composite smeared finite element for mechanics (CSFEM) was formulated which consists of the supporting medium and immersed subdomains of deformable continua with mutual interactions. Interaction is modeled using 1D contact elements (for both tangential and normal directions), where the interaction takes into account appropriate material parameters as well as the contact areas. RESULTS: In this paper we have presented verification examples with applications of the CSFEMs that include the pancreatic tumor tissue, nano-indentation model and tumor growth model. CONCLUSION: We have described CSFEM and contact elements between compartments that can interact. Accuracy and applicability are determined on two verification and tumor growth examples.