An anchor block having within it one or more tunnels through which exercise cords are run and an equal number of slots connected to the tunnels, each slot extending from either the face or the backside of the block. In certain cases, some of the slots may extend from the face while others do so from the backside. In other cases, to enhance strength, all of the slots extend solely from the face or from the backside. This slotted arrangement is useful for a solid handgrip, strapped handgrip assembly, ankle exercise cuff assembly or anchoring door impingement assembly so that stoppered elastic exercise cords may be quickly and easily interchanged. The slot may be shaped in any of several ways including straight, zig-zag or curved.