We aim to develop a minimal physics-based model for cells, which would have application in tissue and tumor growth, wound healing, and embryogenesis. Current physics-based models, including soft-sphere models, Vicsek model, vertex model, and self-propelled Voronoi model, have a number of drawbacks. We have devlopled a more versatile and realistic model based on the “single cell vertex model”. This 2D model solves an number of problems with other similar models including arbitrarily deformable cells with volume and perimeter preserving properties, control over individual cell motions, adjustable cell-cell interactions including attractive, repulsive, and frictional, definable extra-cellular space, and is easily extended to 3D. This model is also interesting outside of the biological arena as a model for deformable particle suspension like emulsions and for packings of deformable particles. For example in deformable polygon packings, we identify a new phase transition between non-confluent and confluent systems that occurs when the particle shape factor is comparable to the average shape factor for Voronoi polygons of disk packings.