Rice (Oryza sativa L.) secretes far smaller amounts of metal-complexing phytosiderophores (PS) than other grasses. But there is increasing evidence that it relies on PS secretion for its zinc (Zn) uptake. After nitrogen, Zn deficiency is the most common nutrient disorder in rice, affecting up to 50% of lowland rice soils globally. We developed a mathematical model of PS secretion from roots and resulting solubilization and uptake of Zn, allowing for root growth, diurnal variation in secretion, decomposition of the PS in the soil, and the transport and interaction of the PS and Zn in the soil. A sensitivity analysis showed that with realistic parameter values for rice in submerged soil, the typically observed rates of PS secretion from rice are sufficient and necessary to explain observed rates of Zn uptake. There is little effect of diurnal variation in secretion on cumulative Zn uptake, irrespective of other model parameter values, indicating that the observed diurnal variation is not causally related to Zn uptake efficiency. Rooting density has a large effect on uptake per unit PS secretion as a result of overlap of the zones of influence of neighbouring roots. The effects of other complications in the rice rhizosphere are discussed. This follows up an earlier paper (Arnold et al., 2010, PCE 33, 370-381) giving evidence for phytosiderophores (PS) involvement in Zn uptake by rice, using isotope discrimination. While the role of PS in Fe uptake by grasses is well established, their involvement in Zn uptake is debated. In this paper, a complete mathematical model of PS-mediated Zn uptake is developed, allowing for root growth, inter-root interaction, diurnal variation in PS secretion, decomposition of the PS in the soil, and the transport and interaction of the PS and Zn in the soil. It shows that (a) measured PS secretion rates are sufficient to explain measured Zn uptake rates and differences between rice genotypes; (b) there is an important interaction with rooting density; but (c) diurnally varying PS secretion has little effect on uptake.