Whether a tumor is metastatic is one of the most significant factors that influence the prognosis for a cancer patient. The transition from a nonmetastatic tumor to a metastatic one is accompanied by a number of genetic and proteomic changes within the tumor cells. These protein-level changes conspire to produce behavioral changes in the cells: cells that had been relatively stationary begin to move, often as a group. In this study we ask the question of what cell-level biophysical changes are sufficient to initiate evasion away from an otherwise static tumor. We use a mathematical model developed to describe the biophysics of epithelial tissue to explore this problem. The model is first validated against in vitro wound healing experiments with cancer cell lines. Then we simulate the behavior of a group of mutated cells within a sea of healthy tissue. We find that moderate increases in adhesion between the cell and extracellular matrix (ECM) accompanied by a decrease in cell-cell adhesion and/or Rho family of small GTPase activation can cause a group of cells to break free from a tumor and spontaneously migrate. This result may explain why some metastatic cells have been observed to upregulate integrin, downregulate cadherin, and activate Rho family signaling.