A glass run for use in a motor vehicle includes an outer side wall, an inner side wall and a bottom wall and has a generally U-shaped cross-section. An outer seal lip and an inner seal lip project from open ends of the outer side wall and the inner side wall into an interior of the glass run. The bottom wall has a shock absorbing lip which obliquely projects from one side end thereof into the interior of the glass run. And a depressed part is formed in an exterior surface of the bottom wall for defining a space with the door frame, and a cushioning member is secured in the depressed part of the bottom wall.