Design codes do not suggest recommendations for the calculations of insert loads and silo wall loads with inserts. Numerical simulations appear to be a promising means to fill this gap. The vertical loads on inserts immersed in wheat contained in a model silo were measured in static and discharge conditions. A flat floor, smooth wall test silo, 1.5 m in height and 0.4 m in diameter, was used. Inserts in the shape of cones, discs, and cylinders were axially suspended on three cords at three heights. A series of discrete element method (DEM) simulations were performed with an assembly of 75,000 spherical particles with a random uniform distribution of diameters with an average of 3.79 ± 0.04 mm placed in the cylindrical container with a diameter of 0.12 m. The set-up of the DEM simulations reproduced the results of the laboratory tests. Despite the very large differences in the number of particles in the real and simulated deposits, the results of simulations and laboratory testing were in good agreement. Thus, DEM was found to be a promising method for the estimation of loads exerted by stagnant or flowing granular material on inserts, as well as for the determination of dead zones and the geometry of the flow channel.