Physically realistic methods are a necessity to close the gap between reality and numerical result in modelling of tumbling mills. A problem is that tumbling mills often operate in a metastable state because of the difficulty to balance the rate of replenishment of large ore particles from the feed with the consumption in the charge. Understanding of the charge motion within the mill is of significance in mill optimisation. Both the breakage of ore particles and the wear of liners/ball media are closely linked to the charge motion. In this work, a ball charge and its interaction with the mill structure is modelled with the smoothed particle hydrodynamic (SPH) method. The mesh free formulation and the adaptive nature of the SPH method result in a method that handles extremely large deformations and thereby suits modelling of grinding charges and pulp liquids. The flexible rubber lifter and the lining are modelled with the finite element method (FEM). A hyper-elastic model governs the elastic behaviour of the rubber. The comminution process is complex and to include all phenomena that occur in a single numerical model is today not possible. Therefore, modelling the physical interaction between charge, mill structure and pulp liquid is the major goal in this work. The SPH-FEM model can predict responses of the mill structure e.g. stress and strain. All parts of the mill system will affect its response and the model gives the opportunity to study the influence of the mill structure and e.g. pressure and shear stresses in the charge. This computational model also makes it possible to predict, the contact forces for varying mill dimensions, liner combinations and pulp densities. By comparing numerical results with experimental measurement from grinding in a pilot mill equipped with an instrumented rubber lifter a validation is done. The deflection profile of the lifters obtained from SPH-FEM simulation shows a reasonably good correspondence to pilot mill measurements as measured by an embedded strain gauge sensor. This model gives information on the grinding process in tumbling mills and better correlation with experimental measurements.