The Kulluk mobile drilling unit "remains grounded but stable" and there is no sign of a fuel spill, incident responders said, vowing to be ready in case of any pollution threat.
The rig was being towed to Seattle when it broke free in heavy seas on New Year's Eve and washed ashore near Kodiak Island, some 300 miles (480 km) southwest of Anchorage.
It has some 150,000 gallons of ultra-low sulfur diesel and roughly 12,000 gallons of oil and hydraulic fluid, according to the far northwestern US state's KTUU television station.
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There is no sign of leaks, but further checks were being made as authorities considered how to salvage the structure, said a Unified Command which includes the US Coast Guard and Shell Alaska.
"The Unified Command plans multiple flyovers today to assess the condition of the Conical Drill Unit (CDU) Kulluk that remains grounded but stable near Sitkalidak Island located on the north edge of Ocean Bay," said an update.
"Once conditions are deemed safe, Unified Command intends to place an assessment team on the Kulluk to further evaluate the vessel's condition," it added, describing the rig as "upright and stable."
Eighteen crew members had already been evacuated from the rig before it broke free late Monday, New Year's Eve, KTUU reported. By Tuesday it was described as "upright and rocking with a slow, but stable motion."
Shell said three people suffered minor injuries during the response to the Kulluk's grounding, according to the television station.
"The extreme weather conditions and high seas continue to be a challenge, said Shell incident commander Susan Childs. "Our priority right now is maintaining the safety of our response personnel and evaluating next steps."
The Federal Aviation Administration (FAA) has set up a no-fly zone around the rig, and the Coast Guard is maintaining a one nautical mile safety zone around it, said the latest update.
Kodiak Island is a few hundred miles from Prince William Sound, where the "Exxon Valdez" oil tanker spilled around 11 million gallons (40 million litres) in March 1989, in one of the world's worst environmental disasters.
