Cell migration occurs in many physiological processes including cancer metastasis, wound healing, and others. Since subcellular forces can play a major role in this process, understanding how they arise and how they affect resulting migration is important. To consider this, we have developed a computational model of a three-dimensional cell migrating across a flat substrate that is capable of providing stress estimates throughout the cell. The model consists of a set of interconnected damped springs or viscoelastic elements. Such elements, and the nodes at which the elements connect with each other, are used to model the cell’s membrane and its interior. We are primarily interested in focal adhesions, structures on the membrane where cells connect to the underlying substrate, because focal adhesion force measurements are experimentally available. To consider these adhesions and their forces we add various components that allow nodes that represent points on the cell membrane to turn into focal adhesions. This includes viscoelastic elements that connect the nodes to the substrate and rules that govern the appearance and disappearance of such adhesions. While multiple strategies can be used to model cell migration and focal adhesion turnover, we believe we have a strategy that represents a reasonable compromise between complexity and simplicity. In addition, it is particularly suitable for calibration using focal adhesion forces and subsequent analysis using tools like sensitivity analysis. In addition to sharing the deformations and forces that our model can predict, we also share a sensitivity analysis to highlight the model’s capabilities. We plan to use the model in the future to better understand the role of forces in the migratory process by correlating force maps with migratory behaviors.