A hand operable scope ring system (10) for mounting a scope (12) on the barrel (14) of a firearm such as a rifle or pistol having a rib (916) with portions having a dovetailed cross-sectional outline and spaced-apart cuts opening on the upper surface of the rib (16). The scope ring system (10) includes a front ring member (24) and a rear ring member (24'). Each ring member has a ring (26) which releasably engages a scope (12). A mount (32) is provided which is mounted on the rib (16) of the barrel (14). The mount (32) has an alignment stud (50) which is received by a registering cut (22) in the rib. This mount defines a cross-sectional portion which receives the dovetailed portion of the barrel rib (16) and includes a threadably advanced securement member (40) which is moved into engagement with the barrel rib (16) for securing the mount in a zeroed position thereon. This position can be determined by the attitude of the lever arms (42) which are operatively associated with each securement member.