Low phosphorus (P) digestibility combined with intensive pig production can increase P diffuse pollution and environmental load. The aim of this paper was to develop a deterministic, dynamic model able to represent P digestion, retention and ultimately excretion in growing and finishing pigs of different genotypes, offered access to diets of different composition. The model represented the limited ability of pig endogenous phytase activity to dephosphorylate phytate as a linear function of dietary calcium (Ca). Phytate dephosphorylation in the stomach by exogenous microbial phytase enzymes was expressed by a first order kinetics relationship. The absorption of non-phytate P from the lumen of the small intestine into the blood stream was set at 0.8 and the dephosphorylated phytate from the large intestine was assumed to be indigestible. The net efficiency of using digested P was set at 0.94 and assumed to be independent of BW, and constant across genotype and sex. P requirements for both maintenance and growth were made simple functions of body protein mass, and hence functions of animal genotype. Undigested P was assumed to be excreted in the feaces in both soluble and insoluble forms. If digestible P exceeded the requirements for P then the excess digestible P was excreted through the urinary flow; thus the model represented both forms of P excretion (soluble and insoluble) into the environment. Using a UK industry standard diet, model behaviour was investigated for its predictions of P digestibility, retention and excretion under different levels of inclusion of microbial phytase and dietary Ca, and different non-phytate P : phytate ratios in the diet, thus covering a broad space of potential diet compositions. Model predictions were consistent with our understanding of P digestion, metabolism and excretion. Uncertainties associated with the underlying assumptions of the model were identified. Their consequences on model predictions, as well as the model evaluation are assessed in a companion paper.