Among the thermodynamic models applicable to solid-liquid-vapor phases, Yokozeki's model is considered as the first repulsion-based analytic equation of state (EOS) in which a discontinuity is introduced in the isotherm. However, it was found that the model violates some physical constraints due to the empirically introduced discontinuity. This work focuses on the evaluation of the empirical basis of the model through scaled-particle theory (SPT) and a modification of the model to satisfy the physical constraint.Keywords Equation of state · Fluid-solid transition · Hard-sphere fluids · Insertion probability Yokozeki [1] presented seven empirically known facts that a unified equation of state (EOS) for solid-vapor-liquid phases should satisfy, and two of them form the basis of the proposed model: (1) the developed EOS should avoid a solid-fluid critical transition and (2) a negative-pressure region is allowed to describe the stability of the solid phase and model the solid-fluid transition via the Maxwell equal-area rule. It is not clear in the author's first paper [1] that the latter requirement holds for the case where the attraction does not exist. However, considering the author's subsequent works [2,3], the latter requirement is expected to hold for the fluids without attractive forces. To satisfy these requirements, Yokozeki considered that "the solid-phase branch in an EOS must be analytically discontinuous at solid-fluid transitions" and modified the repulsive part of the Van der Waals EOS to have two volume limits as follows: