The pressure distribution (PD) and leakage between the slipper and swash plate in an axial piston pump (APP) have a considerable impact on the pump efficiency, affecting aspects such as the load bearing and wear performance of the slipper. Herein, multigene genetic programming (MGGP) and artificial neural network (ANN) machine learning methods (MLMs) are incorporated into a novel approach towards predictive modelling of the PD and leakage on the slipper, which can function hydrostatically/hydrodynamically. Experimentally measured data are used as input for the MGGP and ANN models. The validity of the MGGP and ANN models is verified using test data excluded from the analyses. In addition, the model results are compared with analytic equations (AEs). Both MLMs are found to exhibit strong agreement with the measured data. In particular, the ANN model exhibits superior prediction performance to the MGGP model and AEs.