The excess volume and Gibbs free energy predicted by the scaled particle theory have been calculated for five binary systems of hard spheres, cubes, tetrahedra, ellipsoids and cylinders where the particles of the mixtures have the same shape but different sizes. At a fixed pressure, the excess volume was dependent on the shape of the particles involved, the temperature, pressure and size ratio of the particle. There appeared to be no equivalent sphere which could describe the equation of state and the mixing properties of the systems of non-spherical particles.