A two-dimensional finite element model has been developed to investigate the friction damping characteristics of suspensions with so-called “constant-damping” friction wedges widely used in three-piece bogie wagons in Australia. The model was used to simulate the suspension during pitch modes. The simulation results show that the friction damping force in the suspension pitch modes is dependent on the friction conditions on the wedge contact surfaces, wagon speed, and the wedge shape and elasticity effects including the stuck state. The suspension pitch movements of a three-piece bogie with dry friction wedges can cause wedge rotation and partial separation of wedge contacting surfaces, which seriously affects the wedge friction damping effectiveness. The curved shape of wedge angular surface can significantly improve the friction damping characteristics of three-piece bogie suspensions.