A glass run (10A; 10B; 10C) for use in a motor vehicle, which is capable of preventing seal lips from closely contacting the inner surface of the side walls (34, 36) of the glass run, and accordingly preventing the generation of noise therein. An opening-side groove (64) is formed in an inner surface of an outside wall (34) near an open end thereof to define a space between the inner surface of the outside wall and a base of an outside seal lip (44) when an end of an outside seal lip contacts the inner surface of the outside wall. A bottom-side groove (54) is formed along the inner surface of the outside wall so as to receive the terminal end (52) of the outside seal lip when it is pushed by a door glass (16). A protruding part (60) having at least one rib (62) is further formed along the inner surface of the outside wall so as to contact the generally widthwise middle portion of the outside seal lip when it is pushed by the door glass.