Discrete and continuum modelling of granular flow in a conical hopper discharge is presented. The Discrete Element Method (DEM) is used for discrete modelling and Finite Element Method based on an Arbitrary Lagrangian-Eulerian (ALE) formulation for continuum modelling. The ALE model has shown its capability to model granular flow and macroscopic behaviour in silos in the authors’ previous work (Wang et al., 2013). The use of ALE overcomes mesh distortion problem due to material large deformation which is often encountered in standard finite element modelling of silo discharge. However, there is still limitation when a continuum method is used to model silo discharge, in particular, to pursue particle-scale features in such granular flow. In this study, wall pressure, flow pattern and flow rate during silo discharge are investigated using both ALE and DEM simulation. Classical theories are used as a comparison, to verify the two numerical models. By comparison, it is indicated that both FE model using ALE formulation and DEM model have the capacity to model the granular behaviour and wall pressure for granular process in silos. The conclusion that ALE has advantages over DEM in wall pressure prediction giving stable pressure profile with smooth trend; while DEM has the ability to evaluate the role of particle-scale parameters on macro-scale response in such granular flow after carefully smoothing out the results has been drawn in the present study.