The overall physical properties of tissues emerge in a complex manner from the properties of the component cells and other constituent materials from which the tissue is formed, across multiple length scales ranging from nanometres to millimetres. Recent studies have suggested that interfacial tension between cells contributes significantly to the mechanical properties of tissues and that the overall surface tension is determined by the ratio of adhesion tension to cortical tension. Using cavitation rheology (CR), we have measured the interfacial properties and the elastic modulus of spheroids formed from HEK cells. By comparing the work of bubble formation with deformation of the cell spheroid at different length scales, we have estimated the cortical tension for HEK cells. This innovative approach to understanding the fundamental physical properties associated with tissue mechanics may guide new approaches for the generation of materials to replace or regenerate damaged or diseased tissues.