Solid phase precipitation can greatly affect thermal effects in isenthalpic expansions; wax precipitation may occur in natural hydrocarbon systems in the range of operating conditions, the wax appearance temperature being significantly higher (as high as 350 K) for hyperbaric fluids. Recently, methods for calculating the Joule-Thomson inversion curve (JTIC) for two-phase mixtures, and for three-phase vapor-liquid-multisolid systems have been proposed. In this study, an approach for calculating the JTIC for the vapor-liquid-solid solution systems is presented. The JTIC is located by tracking extrema and angular points of enthalpy departure variations versus pressure at isothermal conditions. The proposed method is applied to several complex synthetic and naturally occurring hydrocarbon systems. The JTIC can exhibit several distinct branches (which may lie within two-or three-phase regions or follow phase boundaries), multiple inversion temperatures at fixed pressure, as well as multiple inversion pressures at given temperature.Keywords Equation of state · Inversion curve · Isenthalpic expansion · Joule-Thomson effect · Multiphase system · Solid precipitation · Wax List of Symbols a Attractive term in the cubic EoS, mixture a i Attractive term in the cubic EoS, component i b Co-volume in the cubic EoS, mixture b i Co-volume in the cubic EoS, component i f i Fugacity, component i