(Solid + liquid) phase equilibria (SLE) of (tridecane + 3-methylpentane or 2,2-dimethylbutane or 1-hexyne or benzene) at pressures up to about 1.0 GPa have been investigated in the temperature range from 293 K to 353 K. A thermostated apparatus was used for the measurements of transition pressures from the liquid to the solid state in two-component isothermal solutions. A polynomial pressure-temperature composition relation for the high-pressure (solid + liquid) equilibria based on the general solubility equation at atmospheric pressure was found to correlate the data satisfactorily. Additionally, the SLE of binary systems (tridecane + 3-methylpentane or 2,2-dimethylbutane or 1-hexyne or benzene) at normal pressure were measured by the dynamic (synthetic) method. The results at high pressure were compared for every system to those at normal pressure. The influence of the hydrocarbons' (with six carbon atoms) structure is discussed. Small effects are observed at high pressure (600 MPa). The main aim of this work was to predict the mixture behavior using only pure-component data and a cubic equation of state for the wide range of pressure studied, far above the pressure range to which cubic equations of state are normally applied. The fluid-phase behavior is described moderately well by the corrected SRK EOS and the van der Waals one-fluid mixing rules.