Many biological processes, including tissue morphogenesis, are driven by cell sorting. However, the primary mechanical drivers of sorting in multicellular aggregates (MCAs) remain controversial, in part because there is no appropriate computational model to probe mechanical interactions between cells. To address this important issue, we developed a three-dimensional, local force-based simulation based on the subcellular element method. In our method, cells are modelled as collections of locally interacting force-bearing elements. We use the method to investigate the effects of tension and cell-cell adhesion on MCA sorting. We predict a minimum level of adhesion to produce inside-out sorting of two cell types, which is in excellent agreement with observations in several developmental systems. We also predict the level of tension asymmetry needed for robust sorting. The generality and flexibility of the method make it applicable to tissue self-organization in a myriad of other biological processes, such as tumorigenesis and embryogenesis.