Based on the Drucker-Prager yield criterion and finite element method, the contact mathematical model was established on wheat and a type of cone-shaped steel-sheet silo. These requirements on the contact surface were solved of the displacement conditions, the pressure transfer and the relations between the pressure and the displacement. Through establishing solving equations and calculation procedures, the reliable results were offered, using Lagrange’s method of multiplier and penalty function method. The results showed that the contact friction stress was small and associated with the contact state. The total contact stress was mainly contact pressure which was increased gradually from the top to the bottom of the silo and showed itself a non-linear relationship.