The present invention relates to a rim member having an internal support member associated with the rim member. The internal support member includes an outer peripheral surface having an annular groove with the groove having a transverse passageway to permit a tire to be mounted onto the rim member. The transverse passageway consists of two angular positions which communicate through an intermediate section on the internal support member. The invention also relates to a tire construction having an internal rolling surface which engages the outer peripheral surface of the internal support member during the run-flat condition.