The spinodal is a locus in the P-V diagram, which is the limit of metastability of a substance with respect to a phase transition. In particular, it is the limit to the negative (tensile) pressure exerted on a liquid, at which the liquid may still be metastable with respect to the gas phase. By requiring that the Helmholtz free energy should be analytic at the spinodal, it is possible to derive the limiting behaviour of thermodynamic properties near the spinodal. In the present paper we show how this analyticity requirement may be used to choose between available equations of state (EOSs). In particular it is shown that the universal equation of state (UEOS) proposed by Vinet et al, complies with the analyticity requirement and may be used to locate the spinodal by extrapolation from within the stable region. The Baonza or 'pseudospinodal' EOS, which is apparently based on the functional form of thermodynamic properties near the spinodal, actually contradicts the analyticity requirement and indeed yields manifestly wrong results in locating the spinodal. However it is shown that the Baonza equation may be viewed as an approximation to the UEOS in states of compression. Its technical importance, which stems from its algebraic simplicity, is also stressed in the present work.