T elastic behaviour of simple monatomic cubic crystals at arbitrary pressure is to be presented in a series of papers. In the present paper, general expressions are derived for calculating the pressure P and the bulk modulus κ as a function of the all-round stretch λ for crystals in which the interatomic interaction energies are modelled by pairwise functions φ. With the aid of a particular family of functions φ, calculations are carried out for the three cubic structures, and a detailed study is made of the influence of crystal structure and explicit nature of φ upon the theoretical elastic behaviour under pressure loading. Calculations are also made of higher order derivatives of P(λ) and gk(λ) in the reference state (i.e. at λ = 1) and the “higher order moduli” thus calculated are used to formulate series expansion approximations to the functions P(λ) and κ(λ). Values of P(λ) and κ(λ) in the series approximations, based upon successively higher order moduli (evaluated in the reference state), are compared with the corresponding “exact” values evaluated in the current state. The theoretical results are useful as empirical relationships modelling the elastic behaviour of crystals at arbitrary pressure.