A structure for mounting an attachment member to a linear motion rolling contact bearing assembly including a bed, a table and a plurality of rolling members interposed between the bed and the table thereby providing a relative motion between the table and the bed. The mounting structure includes an alignment hole defined in the bed or table, a mounting hole defined in the attachment member, a counter member provided with a threaded hole and a bolt extending through the aligned mounting and alignment holes to be threaded into the threaded hole of the counter member with its head in engagement with the attachment member. In the preferred embodiment, the counter member has a contact surface which is substantially the same as and located opposite to a contact surface of the attachment member. In another form, the counter member may be located as sandwiched between the attachment member and the table or bed, in which case the bolt extends through the holes of the table or bed and the counter member to be threaded into the threaded hole of the attachment member.