A ground engaging support structure such as an adapter is mounted on the front edge of an excavating bucket lip in a manner inhibiting side-to-side movement of the installed adapter, and shielding the front bucket lip edge from operational wear at the adapter installation location using opposing tapered block members secured to the front lip edge for movement toward a forwardly projecting stabilizing portion of the lip edge. As the adapter is telescoped onto the front lip edge over its stabilizing projection, correspondingly tapered portions of the adapter engage the block members and move them toward one another and toward the stabilizing projection. Rear leg portions of the adapter are then suitably secured to the bucket lip. The repositioned block members interposed between the adapter the front bucket lip edge then inhibit side-to-side shifting of the installed adapter while also shielding the lip edge from operational abrasion wear.