Abstract: The super-quadric elements based on the continuous function representation can effectively describe the non-spherical particles in nature and industrial applications, and accurately calculate the contact force between the elements through a non-linear iterative method. For the super-quadric elements with complex geometric shapes, the linear contact force model cannot precisely calculate the contact force under various contact patterns. Considering different shapes and surface curvatures between non-spherical elements, a corresponding non-linear viscoelastic contact force model is developed. In this model, the equivalent radius of curvature is introduced to calculate the elastic contact stiffness and viscous force in normal direction. Meanwhile, the elastic force and the viscous force in tangential direction are simplified based on the contact force model of spherical element. To validate the super-quadric algorithms and the contact force model, the normal collision between spherical particles, the oblique contact between ellipsoidal elements, the static packing of cylinders and the dynamic hopper discharge of ellipsoids are simulated with the super-quadric elements. The proposed method is well verified by finite element numerical results and physical experimental data. The non-linear contact force model of super-quadric element with considering the equivalent radius of curvature can accurately calculate the inelastic collision, so as to reasonably reflect the motion law of the non-spherical particle system. Based on the aforementioned method, the effects of aspect ratio and blockiness on the flow characteristics in the discharging process are further analyzed. The results show spherical particles have the fastest flow rate while cube-like particles have the slowest flow rate. Meanwhile, the flow rate of ellipsoids and cylinder-like particles decreases with increasing or decreasing the aspect ratio. In addition, cube-like particles are more likely to form face-face contacts and have a lower flow rate. The super-quadric element with non-linear contact force model can provide an effective numerical approach to simulate the flow characteristics of non-spherical granular materials.