Hurricane Wilma, a Category 4 storm, bashed the tourist resorts of Mexico's Yucatan Peninsula today, its eye crossing over the diving resort of Cozumel as thousands of stranded tourists took refuge in shelters and hotels.

Thousands of residents and tourists had already fled the coastal areas of the Yucatan, which are being battered by hurricane force winds, huge waves and pelting rain, according to the National Hurricane Center's 5 p.m. EDT advisory. The ones who could not get out in time huddled in hotel ballrooms, schools and shelters to wait out the storm. The eye of the hurricane was crossing the northeastern end of Cozumel when the advisory was issued and the northwestern eyewall was on the coast of the Yucatan Peninsula.

Emergency officials in Florida, meanwhile, issued the first evacuation orders for the state's mainland, where the storm is expected to head after making landfall in Mexico. The mandatory order, effective noon today, covered part of the west coast city of Naples and the nearby towns of Marco Island and Everglades City. It was not immediately clear how many residents were covered under the order, but many were already leaving, according to news agency reports.

"Today's message is really to prepare and stay aware," Gov. Jeb Bush (R) told reporters in Tallahassee, the Associated Press reported. "I understand it can be really frustrating."

"The most important thing now . . . is to protect lives," Mexican President Vicente Fox said in a broadcast address to his nation last night.

Wilma, a powerhouse storm churning winds of near 140 mph extending outward up to 85 miles, was moving about 5 mph northwest. The Yucatan is a popular tourist and cruise ship destination because of its long stretches of white sand beaches and Mayan ruins.

"The center of Wilma is expected to move inland over the extreme northeastern Yucatan Peninsula tonight and remain inland on Saturday," the hurricane center said in its latest advisory. It was expected to weaken after moving ashore.

The hurricane center said rain of up to 40 inches is possible in isolated sections of the Mexican peninsula and parts of Cuba through Sunday. A storm surge of up to 11 feet above normal tide levels is also expected.

Mexico evacuated residents and tourists from its coast, set up shelters and put the army on alert, Interior Minister Carlos Abascal said, according to news agencies. About 1,000 tourists stayed on Cozumel, where the airport was closed, news agencies reported.

The hurricane is expected to veer right toward Florida's western coast after smacking into Mexico. But computer models are differing over when that might happen, which will affect how big the storm is when it hits the United States, according to Max Mayfield, director of the National Hurricane Center in Miami.

Mayfield said if Wilma lingers over the Yucatan, it will probably weaken into a Category 2 or Category 1 storm by the time it reaches Florida, now predicted for sometime Monday. If it just nicks the Yucatan and then veers Florida, Wilma could keep its strength and move quickly toward the U.S. mainland. Mayfield said the most likely scenario is that it will stall over the Yucatan, completely hammering the Mexican tourist region, for at least 24 hours.

"It's going to be a long couple of days for the Yucatan," Mayfield predicted. But that stall will help weaken the storm, he said.

"By this time tomorrow, we'll have a much weaker hurricane than we have today," he said after the latest advisory was issued.

Mayfield said he expects a hurricane watch to be issued for the Florida peninsula tomorrow, and he reminded residents to not focus only on the center of the hurricane because the storm system is about 200 miles wide. The center's advisory noted that outer rain bands from Wilma are affecting portions of Florida, especially the Keys, with 2 to 4 inches of rain through Sunday.

Emergency officials for Monroe County, which includes the Florida Keys, urged residents to get out before the road to the Keys becomes inundated with water from a storm surge.

"Those in the Keys deciding to ride this storm out, remember that there's nowhere inland to go," said Billy Wagner, a Monroe County emergency management official. "You're going to be there for the duration of the system."

The center's advisory said Wilma has already spawned large swells in the Gulf of Mexico that will likely affect portions of the northern Gulf Coast later today.

Storm-weary Floridians boarded up homes and stocked up on emergency supplies ahead of the sixth hurricane to hit their state in the past year. Most tourists fled the Florida Keys after an evacuation order was imposed for tourists two days ago.

Florida is still recovering from last year's record four hurricanes, which caused billions of dollars in property damage.

FEMA's acting director, R. David Paulison, urged people evacuating to take important papers, such as bank statements, checkbooks, insurance documents, birth certificates and credit cards, with them.

"Put it all in a plastic bag so it'll be safe," Paulison said at a news briefing at FEMA headquarters in Washington.

He urged residents to fill their cars up with gas and buy extra batteries for their radios. He advised having three days of food and water on hand, as well as any necessary medicine. He said there is no shortage of fuel in Florida, and FEMA is pre-positioning food, water and ice there.

"We're expecting the unexpected," Paulison said. He admitted that during Hurricane Katrina, FEMA lacked "good situational awareness" of what was happening on the ground. He said that would not happen this time around.

White House officials said today the federal government is prepared for a quick aid response in Florida, if needed. Frances Fragos Townsend, President Bush's homeland security adviser, told reporters that FEMA and other federal agencies will have more communications gear, emergency supplies and people in Florida because of lessons learned from the problems with Hurricane Katrina, which hit Mississippi and Louisiana in August, according to AP.