Explicit functions are widely used to interpolate, extrapolate, and differentiate theoretical or experimental data on the equation of state (EOS) of a solid. Two new theoretically motivated EOS functions are presented here. The simplest realistic model for a simple metal, the stabilized jellium (SJ) or structureless pseudopotential model, is the paradigm for the Stabilized Jellium Equation Of State (SJEOS). A simple metal with exponentially-overlapped ion cores is the paradigm for an augmented version (ASJEOS) of SJEOS. For the three solids tested (Al, Li, Mo), ASJEOS matches all-electron calculations better than prior equations of state. Like most of the prior EOS's, ASJEOS predicts pressure P as a function of compressed volume v from only a few equilibrium inputs: the volume v 0, the bulk modulus B0, and its pressure derivative B1. Under expansion, the cohesive energy serves as another input. An advantage of the new equation of state is that these equilibrium properties other than v0 may be found by linear fitting methods. The SJEOS can be used to correct B0 and the EOS found from an approximate density functional, if the corresponding error in v0 is known. The typically-small contribution of phonon zero-point vibration to the EOS is also estimated, as well as it is shown that the physical hardness Bv does not maximize at equilibrium, and that the 'ideal metal' of Shore and Rose is the zero-valence limit of stabilized jellium