A model with few material parameters is proposed for finite element simulation of the transient flow of cohesionless granular materials in silos. The constitutive model used is essentially a fluid model and, consequently, it is best established in the Eulerian format. The model allows the simulation of initial stress transients at the beginning of the discharging process. After long time, when the solution approaches steady state, the flow pattern that is developed represents either a mass or funnel flow situation. Numerical examples of transient stress fields are given, and the flow patterns in advanced silo geometries are studied. The numerical results are in good agreement with analytical solutions and experiments known from the literature.