The brake shoe support assembly is able to track the lateral movement of a wheel, typically a wheel on an axle truck that allows lateral wheel movement. In operation, a flange of the wheel pushes on one side of the brake shoe support assembly, pushing it along a pin, and compressing a resilient biasing structure. As the wheel returns to a center or neutral position, the compressed resilient biasing structure expands pushing the brake shoe support assembly back to an original or neutral position. The resilient biasing structure also minimizes the lateral movement of the brake shoe support assembly down the wheel taper under normal braking loads thus preventing shoe ride-off. The resilient biasing structure may be enclosed in a housing adapted to prevent the intrusion of contaminants.