A damper mount structure comprising: a rod of a damper of a suspension system, the rod having an end portion; a vehicular body panel having a lower surface facing downwardly of a vehicle, and an opening portion, the end portion of the rod being inserted through and fastened to the opening portion; an upper stationary disk facing toward an upper surface of the vehicular body panel and subjected to a pressure of a nut screwed onto the end portion of the rod; a lower stationary disk facing toward the lower surface of the vehicular body panel and opposed to the upper stationary disk with the vehicular body panel interposed between the upper stationary disk and the lower stationary disk; an annular upper damping member contacting the vehicular body panel and compressed by the upper stationary disk, the end portion of the rod fitting through the annular upper damper; an annular lower damping member which is disposed between the vehicular body panel and the lower stationary disk and is in contact with the lower stationary disk; an annular projection protruding from the lower damping member toward the upper damping member, the projection having an outer diameter smaller than an outer diameter of the lower damping member; and a collar which is integrally fixed to the lower surface of the vehicular body panel and has an inner circumferential surface disposed around an outer circumferential surface of the projection, the collar having one end surface and an opposite end surface, the one end surface being contiguous with the inner circumferential surface and fixed to the vehicular body panel, the collar having a height (Hc) from the opposite end surface to the one end surface, the height of the collar being substantially equal to a height (Hb) of the projection, characterized in that the collar and the projection are disposed below the opening portion, the opening portion of the vehicular body panel contacting the upper damping member has a beveled corner, wherein the beveled corner is contiguous with the upper surface of the vehicular body panel and faces toward the upper damping member. a rod of a damper of a suspension system, the rod having an end portion; a vehicular body panel having a lower surface facing downwardly of a vehicle, and an opening portion, the end portion of the rod being inserted through and fastened to the opening portion; an upper stationary disk facing toward an upper surface of the vehicular body panel and subjected to a pressure of a nut screwed onto the end portion of the rod; a lower stationary disk facing toward the lower surface of the vehicular body panel and opposed to the upper stationary disk with the vehicular body panel interposed between the upper stationary disk and the lower stationary disk; an annular upper damping member contacting the vehicular body panel and compressed by the upper stationary disk, the end portion of the rod fitting through the annular upper damper; an annular lower damping member which is disposed between the vehicular body panel and the lower stationary disk and is in contact with the lower stationary disk; an annular projection protruding from the lower damping member toward the upper damping member, the projection having an outer diameter smaller than an outer diameter of the lower damping member; and a collar which is integrally fixed to the lower surface of the vehicular body panel and has an inner circumferential surface disposed around an outer circumferential surface of the projection, the collar having one end surface and an opposite end surface, the one end surface being contiguous with the inner circumferential surface and fixed to the vehicular body panel, the collar having a height (Hc) from the opposite end surface to the one end surface, the height of the collar being substantially equal to a height (Hb) of the projection, the collar and the projection are disposed below the opening portion, the opening portion of the vehicular body panel contacting the upper damping member has a beveled corner, wherein the beveled corner is contiguous with the upper surface of the vehicular body panel and faces toward the upper damping member.