This paper presents the methodology of the indicator function–discrete elements probability density function statistical average applied to Two–phase flow modelling. This formulation allows to consider particles of arbitrary shape and size and it can be applied to any laminar or turbulent flow. In the case of equal sized spherical dispersed elements, the most common case found in the literature, the final expression for the interaction terms (contributions that describe the effect of the second phase on the continuous one) are obtained without great difficulties due to the high isotropy of the spherical shape. This task, in the general case of non–spherical non–equal particles is no longer straightforward and the derivation of the appropriate general interaction terms is presented in §4. In the case that the dispersed elements are small enough, some simplifications can be further introduced leading to a final presentation