A collapsible rack or stand for supporting a bicycle or the like in an upright position includes a pair of supports that are pivotably interconnected together for movement between an open, operative position and a closed, inoperative position. Each support defines one or more vertically extending spaces, each of which is configured to receive one of the bicycle wheels for supporting the bicycle in an upright position when the supports are in the open, operative position. Each support includes a lower member and an upper member, between which the wheel-receiving spaces are located, and the upper members of the supports are pivotably interconnected via a hinge arrangement for enabling movement of the supports between the open, operative position and the closed, inoperative position. The hinge arrangement is in the form of a hinge barrel secured to the upper member of each support, and the hinge barrels define aligned passages through which a hinge pin extends. The hinge barrels are configured and arranged such that the upper members of the supports are moved into engagement with each other when the supports are moved away from the closed, inoperative position so as to place the supports in the open, operative position, thus providing a stop for consistently positioning the supports in a predetermined angular relationship when the supports are moved to the open, operative position. The supports may be identically constructed, and are preferably connected together so that the spaces of the supports are offset from each other to enable bicycle wheels to be engaged with the supports in a staggered manner from opposite sides of the stand.