The method of characteristics has been used to predict the exact stress and velocity fields in an incompressible, cohesionless, Coulomb material discharging from a conical hopper for a great variety of boundary conditions imposed on the top surface. It is found that in all cases the stresses and velocity tend to the radial stress and velocity fields and that convergence is achieved about half way down the hopper. This justifies the use of the radial stress field in Jenike’s design method. The velocity fields often show regions of more or less constant velocity separated by velocity characteristics. This justifies the assumptions in Drescher’s method of predicting velocity distributions.