an outer side wall, an inner side wall and a bottom wall, which define a generally U-shaped cross-section;

an outer seal lip and an inner seal lip which respectively project from distal ends of said outer side wall and said inner side wall into an interior defined by said outer side wall, said inner side wall and said bottom wall;

said bottom wall including a shock absorbing lip which obliquely projects from one of an inner side end and an outer side end of said bottom wall into said interior, and a depressed part provided in an exterior surface thereof for defining a space with the door frame; and

a cushioning member which is provided in said depressed part of said bottom wall,

wherein said shock absorbing lip curves convexly toward an opening of the glass run such that when an end of the door glass contacts said shock absorbing lip, a tip end of said shock absorbing lip contacts an interior surface of said bottom wall and forms a tubular part defined by said shock absorbing lip and said bottom wall, said tubular part is adapted to absorb shock caused by the pushing of said end of the door glass against said tubular part, said bottom wall is adapted to extend obliquely to the door frame to define said space with the door frame, a cross section of said space gradually enlarges from said inner side end to said outer side end of said bottom wall, said bottom wall is arranged such that when said glass run is attached to the door frame, said inner side end of said bottom wall, which is connected to said inner side wall, contacts the door frame, whereas said outer side end of said bottom wall, which is connected to said outer side wall, does not contact the door frame, and when said end of the door glass pushes said bottom wall, said outer side end of said bottom wall contacts the door frame and said cushioning member is compressed, thereby absorbing shock caused by the pushing of said end of the door glass against said bottom wall, and said bottom wall includes a central part, an outer side part and an inner side part, said outer side part and said inner side part are integrally formed with said central part, a portion of said outer side part bends and is connected to a base end of said outer side wall, and a seal lip projects from said outer side part of said bottom wall over said depressed part in such a manner as to contact the door frame when said end of the door glass pushes said bottom wall, and wherein said cushioning member is partially disposed between said seal lip and said bottom wall in a direction defined by a raising and lowering direction of the door glass.