© 2015 Elsevier B.V. The uptake of K by crops depends on dynamic interactions between soil and fertiliser K availability, season effects on growth, agronomic management and soil properties. In such complex systems, simulation modelling which accounts for both K supply and demand processes may be the most effective approach to assessing the efficacy of different K fertiliser strategies for crop uptake. We developed a K model for wheat in the crop simulation model APSIM. Reactive solute transport was modelled using the mixing cell approach and root K uptake was modelled based upon the concentration of K in the root system and soil solution and an equilibration between root and shoot concentrations. Photosynthetic assimilation rate and water-use efficiency were modified according to shoot K concentration. The parameter optimisation software PEST was applied to optimise the parameters introduced for this model. Overall the model provided a satisfactory match to the calibration data set for soil surface K, grain yield and shoot K concentration in early growth stages but model predictions were most sensitive to the parameter that describes the shape of the K adsorption isotherm. Evaluation of the calibrated model for an independent data set (n=807) showed reasonable agreement with maturity biomass (r2=0.73, RMSE=1666kgha-1), soil surface K in the year after application (r2=0.72, RMSE=17mgkg-1), and grain yield (r2=0.66, RMSE=637kgha-1). However, it was necessary to modify the grain fill function to include the effect of shoot K concentration on grain filling rate which led to an improvement in grain yield prediction at low K fertiliser rates and in the relative response to K fertiliser application. The current K simulation model provides satisfactory predictions of wheat response to K on sands across a range of seasons. Further improvement could be achieved by evaluation of the solute transport model under field conditions and the grain fill function; both improvements require data sets of wheat K response from experimental sites with well characterised soil water properties.