The paper presents the analysis of flow conditions of cohesive and cohesionless bulk materials in a conveyor discharge point of a flat conveyor belt. The analysis was carried out for stationary flows at high velocities. It presents mathematical methods for the description of the velocity of a material leaving a throwing point of a flat conveyor belt as well as final equations which enable the determination of velocity of the material after it has left the throwing point (with the accuracy sufficient for practical use). Next, the velocity calculated for the proposed mathematical description (for selected material groups) has been compared with the velocity obtained from mathematical relations commonly used by engineers. The proposed equations for determining the velocity of the material beyond the point have proved useful, since they enable excluding the indirect equations. Finally, the difference between the values of the velocity obtained with the proposed and indirect equations have been determined and the relative error for the proposed method has been calculated.