Abstract: We have analysed the response of cells on a bed of micro-posts idealized as a Winkler foundation using a homeostatic mechanics framework. The framework enables quantitative estimates of the stochastic response of cells along with the coupled analysis of cell spreading, contractility and mechano-sensitivity. In particular the model is shown to accurately predict that: (i) the extent of cell spreading, actin polymerisation as well as the traction forces that cells exert increase with increasing stiffness of the foundation; (ii) the traction forces that cells exert are primarily concentrated along the cell periphery; and (iii) while the total tractions increase with increasing cell area the average tractions are reasonably independent of cell area, i.e. for a given substrate stiffness, the average tractions that are normalized by cell area do not vary strongly with cell size. These results thus suggest that the increased foundation stiffness causes both the cell area and the average tractions that the cells exert to increase through higher levels of stress-fibre polymerization rather than the enhanced total tractions being directly linked through causation to the larger cell areas. A defining feature of the model is that its predictions are statistical in the form of probability distributions of observables such as the traction forces and cell area. In contrast, most existing models present solutions to specific boundary value problems where the cell morphology is imposed a priori. In particular, in line with observations we predict that the diversity of cell shapes, sizes and measured traction forces increase with increasing foundation stiffness. The homeostatic mechanics framework thus suggests that the diversity of observations in in vitro experiments is inherent to the homeostatic equilibrium of cells rather than being a result of experimental errors.