An equipment carrier adapted for mounting to a support member associated with a vehicle, includes a base engageable with the support member and a universal mounting arrangement for securing the base to the support member. The universal mounting arrangement includes a flexible retainer member, such as a retainer strap, that extends from and is engageable with a clamping member movably mounted to the base. The retainer strap defines a free end that extends from one side of the base, and which is adapted to be wrapped about the support member and engaged with a releasable engagement arrangement associated with the clamping member. The retainer strap and the releasable engagement arrangement define a variable effective length of the retainer strap when the retainer strap is initially wrapped about the support member. An actuator member, such as a rotatable threaded member, is engaged with the clamping member and with the base for moving the clamping member away from the base. Movement of the clamping member away from the base functions to introduce tension into the retainer strap, to force the base against the upper surface of the support member and to draw the retainer strap into engagement with the support member. In this manner, the base is securely clamped onto the support member, to mount the equipment carrier to the support member. The flexibility of the retainer strap and the variable effective length provided by engagement of the retainer strap with the clamping member enables the retainer strap to be wrapped about a support member having any shape and configuration, to allow the equipment carrier to be mounted to various types of original equipment or retrofit support members.