A variable bore packer used in a blowout preventer to form a seal against different diameter tubular members for oil and gas drilling operations. The variable bore packer includes a packer member molded of elastomeric material with certain mechanical properties and including an inside curved surface. The packer also includes a plurality of packer inserts molded within the packer member to form an insert array. Additionally, the packer includes a protrusion extending from and bonded to the packer member inside curved surface, the protrusion including increased mechanical properties compared to the packer member. The packer member, the insert array, and the protrusion are molded into a unitary structure and sized to form a seal against the different diameter tubular members upon closure of the blowout preventer. Also, the insert array and the protrusion diminishing extrusion of the elastomeric material between the packer inserts and the tubular members.