Flash calculation plays significant roles in petroleum and chemical industries. Since Michelsen proposed his milestone studies in 1982, through several decades of development, the current research interests on flash calculation have been shifted from accuracy to efficiency, but the ultimate goal remains the same; that is accurate determination of equilibrium phase amounts and compositions at a given condition. On the other hand, finding the transition route and its related saddle point is often crucial to understand the whole energy landscape of flash models, which would provide new insights for designing numerical algorithms or optimizing existing ones. In this study, an efficient numerical approach is developed by coupling the string method with the exponential time differencing (ETD) scheme to investigate the minimum energy paths and first-order saddle points of VT flash models with Peng-Robinson equation of state. As a promising alternative to the conventional approach, VT flash calculates phase equilibria under a new variable specification of volume and temperature. The Rosenbrock-type ETD scheme is used to reduce the computational difficulty caused by the high stiffness of the model systems. The proposed ETD-String method successfully calculates the minimum energy paths of single-component and two-component VT flash models with strong stiffness. Numerical results also show good feasibility and accuracy in calculation of equilibrium phase amounts and compositions.