The mechanism of the bainitic transformation in copper-based alloys has been in a long-standing controversy, because a contribution of lattice shearing to the transformation has been suggested or questioned by different researchers. In order to clarify the role of lattice shearing, the transformation process under applied stress at various temperatures between 423 and 473 K was traced in a Cu-Zn-Al alloy by measuring the electrical resistivity. Since the resistivity increases with increasing amount of transformation products, a quantitative evaluation of transformation kinetics can be made by this method. It has been found that the transformation is highly sensitive to the aging temperature, and that the activation energy is close to that of solute diffusion in the alloy. It is also evident that the applied stress accelerates the transformation, while it does not affect the activation energy. This acceleration clearly indicates that the transformation proceeds by lattice shearing. It is concluded that diffusion-controlled lattice shearing is the most plausible mechanism of the bainitic transformation. The effect of applied stress on the transformation rate is discussed in terms of the free energy change due to stressing.