The paper presents a novel approach for the solution of the isothermal multiphase flash problem with particular application to systems exhibiting liquid-liquid-vapor equilibria. The approach includes a rigorous method for thermodynamic stability analysis as a first step and an efficient phase identification procedure. The stability analysis, exercised only once, uses a modification of the Gibbs tangent plane criterion. The identification procedure implements the results of the stability test in a sequence of Liquid-liquid and liquid-vapor calculations only till the phase configuration with a minimum Gibbs energy is determined. The efficiency and reliability of the proposed new method is illustrated by solving three typical problems encountered in enhanced oil recovery, natural gas processing and petrochemical industry.