A specimen tube storage rack includes a hollow housing having a plurality of wells formed in the top wall and extending into the interior of the housing. An assembly of three parallel plates is mounted in an upper portion of the housing, with the top plate forming the top wall of the housing. Each plate has a plurality of openings formed therein which are vertically coaxial to form the wells. A pair of sheets of resilient flexible material are compressed between pairs of plates, and include a plurality of apertures coaxial with the openings in the plates. The apertures in the sheets have cuts extending radially outwardly into the sheet, to form flaps surrounding each aperture. The compression of each sheet between a pair of plates urges the flaps to a generally coplanar position. The apertures in the sheets are smaller in diameter than the openings in the plates, and smaller in diameter than the test tubes inserted into the wells, such that the flaps will be bent downwardly as the test tubes are inserted in each well. The urging of the flaps to a coplanar position thereby exerts a biasing force on the test tubes to center and plumb the test tubes, and to apply a restraining force against removal of the test tubes from the wells.