A numerical method for direct simulations of boiling flows is presented. The method is similar to the front tracking/ finite difference technique of Juric and Tryggvason [Int. J. Multiphase Flow 24 (1998) 387], where one set of conservation equations is used to represent the mass transfer, heat transfer, and fluid flow in the liquid and the vapor, but improves on their numerical technique by elimination of their iterative algorithm. The justification of the mathematical formulation is presented and the numerical method and the code is validated by comparison of the results with the exact solutions of a few analytical problems. A grid refinement test for film boiling on a horizontal surface shows the convergence of results. (C) 2004 Elsevier Ltd. All rights reserved.