We present a new approach to measuring cell-generated forces from the deformations of elastic microspheres embedded within multicellular aggregates. By directly fitting the measured sensor deformation to an analytical model based on experimental observations and invoking linear elasticity, we dramatically reduce the computational complexity of the problem, and directly obtain the full 3D mapping of surface stresses. Our approach imparts extraordinary computational efficiency, allowing tractions to be estimated within minutes and enabling rapid analysis of microsphere-based traction force microscopy data.