In this work, we develop an alternative two-phase flash algorithm with the consideration of capillary pressure at specified mole numbers, volume, and temperature. This algorithm is built upon the volume-temperature (VT) two-phase flash algorithm as proposed by Mikyška and Firoozabadi (2012), which relies on the use of the newly defined volume function and volume function coefficient. Our algorithm contains two loops: an inner loop and an outer loop. In the inner loop, the interior point method is used to solve the vapor-phase fraction by minimizing the objective function. In the outer loop, the volume fraction of the vapor phase is updated by solving the pressure equilibrium equation which simultaneously considers the capillary pressure between the two phases; herein, we first divide the interval (0, 1) to 1000 subintervals and then apply the bisection method in each subinterval. This method is used to robustly solve the pressure equilibrium equation. The capillary pressure is calculated using the Young-Laplace equation on the basis of the interfacial tension predicted by the parachor model. Eventually, knowing the volume fractions enables one to update the equilibrium ratios in the outer loop. We demonstrate the correctness and robustness of our algorithm by testing it against four fluid mixtures, including binary and ternary mixtures. The two-phase envelope obtained from the VT-flash algorithm with capillarity effect has shown excellent agreement with that calculated by the pressure-temperature (PT) flash algorithm with capillarity effect. In addition, we examine the influence of capillary pressure on the two-phase envelope in the molar-density/temperature (cT) space.