In this paper. we propose a mathematical study of the virial expansion of cubic equations of state. We attempt to provide an answer to the following questions: -Is the virial equation only appropriate for the description of gases at low to moderate densities? -What is the impact of the order of truncation on the representation of P - v isotherms? -What is the difference between a truncation at an even order and a truncation at an odd order? -What is the theoretical volume range of validity of a virial expansion? To illustrate and apply these concepts, we considered four classical cubic equations of state, namely: Van der Waals, Redlich-Kwong-Soave, Peng-Robinson and Schmidt-Wenzel. For all of these equations, we detail the limitations and the capabilities of the virial expansions. Finally, we propose a new general relation between the coefficients of the virial equation in pressure and those of the virial equation in density. (C) 2009 Elsevier B.V. All rights reserved.