A glass run and mounting structure therefor for installation in an automotive vehicle includes a metal glass run channel (11) being C-shaped and having resilient seal lip portions (12,13) disposed along facing edges of an open side and an elongate edge seal portion (14) disposed along an inner bottom surface opposite the open side. This pre-assembled glass run assembly is joined to a mounting bracket (4) to be attached at an operational position on a structural member of vehicle body or the like. For effecting attachment of the channel (11) and bracket (4), the flat metal bottom surface of the channel (11) is overlaid on a metal plate portion (4b) of the bracket (4) at a predetermined joining position. Then, punch processing is carried out for simultaneously plastically deforming both the bottom surface of the channel (11) and the plate surface (4b) of the bracket (4) for effecting secure attachment therebetween. The elasticity of an EPDM material selected for the edge seal portion (14) is such that it will not be torn or damaged by the punch processing operation.