(Solid + liquid) phase equilibria (SLE) of (n-hexadecane, or n-octadecane + 3-methylpentane, or 2,2-dimethylbutane, or benzene) at very high pressures up to about 1.0 GPa have been investigated at the temperature range from T = (293 to 353) K. The thermostated apparatus for the measurements of transition pressures from the liquid to the solid state in two component isothermal solutions was used. The pressure-temperature-composition relation of the high pressure (solid + liquid) phase equilibria, polynomial based on the general solubility equation at atmospheric pressure was satisfactorily used. Additionally, the SLE of binary systems (n-hexadecane, or n-octadecane + 3-methylpentane, or 2,2-dimethylbutane, or benzene, or n-hexane or cyclohexane) at normal pressure was discussed. The results at high pressures were compared for every system to these at normal pressure. The influence of the size and shape effects on the solubility at 0. 1 MPa and high pressure up to 600 MPa was discussed. The main aim of this work was to predict the mixture behaviour using only pure components data and cubic equation of state in the wide range of pressures, far above the pressure range which cubic equations of state are normally applied to. The fluid phase behaviour is described by the corrected SRK-EOS and the van der Waals one fluid mixing rules. (c) 2005 Elsevier Ltd. All rights reserved.