(Reuters) - Tornadoes that struck the United States from May 18 to May 20 caused between $2 billion to $5 billion of insured losses, disaster modeling company Eqecat said late Thursday.

At the high end of the range, the tornado outbreak may rank as the second-worst ever in terms of insured losses, behind the late-April 2011 twisters that devastated Tuscaloosa, Alabama, and other communities.

Eqecat said most of the losses were attributed to the tornado that devastated Moore, Oklahoma, on Monday. That storm, with winds that exceeded 200 miles per hour, killed 24 and flattened two elementary schools.

Some 76 tornadoes struck across 10 states over a three-day period, said Eqecat, whose models are used by the insurance industry to forecast losses. The worst of it was in Moore, where the firm said about 13,000 structures were damaged.

Oklahoma's insurance commissioner, John Doak, said earlier this week he expected damage from the Moore tornado to exceed $3 billion on its own.

The brunt of those losses is likely to fall on insurers State Farm and Farmers Insurance Group, which together have an aggregate market share of nearly 29 percent in the state, according to SNL Financial.

Over the last two years, tornadoes have become a huge loss driver for the insurance industry. The German reinsurer Munich Re has estimated tornadoes caused about $40 billion in insured losses in the United States in 2011 and 2012.

Since 1980, average thunderstorm losses, including tornadoes, have risen sevenfold.

(Reporting by Ben Berkowitz; Editing by Jeffrey Benkoe and Bernadette Baum)