(CNN) -- Hurricane Paloma became an extremely dangerous Category 4 storm Saturday morning, raising the specter of destroyed buildings, downed trees and flooded streets in the Cayman Islands, Cuba and beyond.
The storm lashed Little Cayman and Cayman Brac -- two of three islands that make up the Cayman Islands -- with heavy rain and winds that howled at speeds of up to 135 mph (217 kph), the National Hurricane Center in Miami, Florida, said.
Forecasters expect the storm to roar on toward Cuba, possibly strengthening Saturday morning before losing some steam later Saturday and Sunday.
At 5:30 a.m. ET Saturday, the storm's center was near Cayman Brac. It was 95 miles (152 kilometers) east-northeast of Grand Cayman and about 175 miles (281 kilometers) southwest of Camaguey, Cuba, the hurricane center said.
A Category 4 hurricane can blow down trees, tear off roofs, destroy mobile homes and cause major damage to the lower floors of structures near the shore. The strongest storms are Category 5 hurricanes.
Forecasters said they expect Hurricane Paloma's center to approach the Cuba coast Saturday night or Sunday morning. They warned the hurricane also could affect people in the Bahamas and Jamaica.
J.B. Webb, a manager at a radio station on Grand Cayman, said some residents went to shelters Friday night while others shut themselves in businesses that had recently been rebuilt to withstand a Category 5 hurricane.
A hurricane warning covered the Cayman Islands as well as the Cuban provinces of Sancti Spiritus, Ciego de Avila, Camaguey and Las Tunas on Saturday, the hurricane center said. A warning means hurricane conditions are expected within 24 hours.
Authorities issued a tropical storm warning for the Cuban provinces of Holguin and Santiago de Cuba.
The storm's projected path would steer it away from the U.S. mainland and out into the Atlantic.
The storm is expected to produce rainfall accumulations of 5 to 10 inches over the Cayman Islands and central and eastern Cuba, with 15 inches possible in some areas. Flashfloods and mudslides are possible, forecasters said.
Cuban television was broadcasting messages telling viewers not to cross swollen rivers, to avoid fallen cables, and to evacuate if told to do so by Civil Defense officials.
In Las Tunas, students in boarding schools were sent home, and the schools will be used as shelters.
Evacuations were under way in some coastal areas prone to flooding. Rice and cereal were being shipped to other parts of the country to prevent spoiling, and no tourists were being allowed to enter many areas.
(CNN's Morgan Neill in Havana, Cuba and Rory Suchet in Atlanta, Georgia contributed to this report.)