Mechanical interactions between cells and extracellular matrix (ECM) mediate epithelial cyst formation. This work relies on the combination of numerical modeling with live cell imaging, to piece together a novel nonintrusive method for determining three-dimensional (3D) mechanical forces caused by shape changes of a multicellular aggregate at the early stages of epithelial cyst formation. We analyzed the evolution of Madin-Darby canine kidney cells in 3D cultures using time-lapse microscopy, with type I collagen gel forming the ECM. The evolving 3D interface between the ECM and the cell aggregate was obtained from microscopy images, and the stress on the surface of a proliferating aggregate and in the surrounding ECM was calculated using the finite element method. The viscoelastic properties of the ECM (a needed input for the finite element method solver) were obtained through oscillatory shear flow experiments on a rheometer. For validation purpose, the forces exerted by an aggregate on a force-sensor array were measured and compared against the computational results.