Unified Command said the drill ship remains stable as it oversees preparations to tow the vessel to harbor for repairs.
Kulluk struck ground during rough weather in late December while en route to Seattle. No oil spill or injuries were associated with the incident.
"The Unified Command has received confirmation from naval architects that the damage sustained by the grounding poses no threat to the stability or integrity of the Kulluk while anchored in Kiliuda Bay," a statement read. "The next step is an analysis of this data to determine the best course of action to relocate the Kulluk for permanent repairs."
The U.S. Interior Department last year signed off on Shell's exploration plans for the arctic waters off northern Alaska. Extreme weather conditions and a series of equipment issues complicated the company's exploration campaign.