Sunday is Father’s Day, and chances are you will be taking Dad out to dinner (after all, didn’t you take Mom out on Mother’s Day?)

To that end, the backers of the inaugural Martha’s Vineyard Restaurant Week hope they are onto something, because Sunday is the kickoff night for a weeklong event designed to attract hungry diners with interesting menus at reasonable prices.

Over 20 restaurants are signed up to participate in the first annual restaurant week on the Island, and at press time the number was still growing. Participation is free, and restaurants can sign up through Saturday. The week begins Sunday and runs through Thursday. Each restaurant designs a three-course fixed price menu that costs between $25 and $45. Menus are on the restaurant week Web site (marthasvineyardrestaurantweek.com ) . The event is sponsored by the Martha’s Vineyard Chamber of Commerce and every major media outlet on the Vineyard, including Martha’s Vineyard Online, MVY radio, Plum TV, and the two Island newspapers.

“[We] started talking about it two years ago,” said Dawn Bellante-Holand, general manager of Martha’s Vineyard Online and a key organizer. “We’re always thinking of ways that we can do more business or bring more of the Vineyard experience to people. Restaurant Week seemed to be the perfect concept to introduce on the Island . . . This year, with the economy making a lot of people wonder how the season would unfold, it seemed like a good time to try something different,” she said.

For diners, the week provides an opportunity to try restaurants they may not have otherwise. For restaurant owners, it offers the chance to stimulate business during what is usually a lull — after Memorial Day and before the Fourth of July. “It’s a great opportunity for the chefs to be creative and to do something a little unusual . . . and just kind of challenge themselves,” said Ms. Bellante-Holand.

“It’s a celebration of Island chefs, restaurants, and the art of dining. You can go into any one of the restaurants that are participating and know that you are going to have a great experience,” she added.

The restaurants range from high-end fine dining locales like the Sweet Life Café in Oak Bluffs to more casual and family-friendly places like Sharky’s.

“I want to be more approachable,” said Sweet Life owner Susan Guerin, of her decision to participate. “Hopefully we will get people in here who have wanted to come but don’t.” The higher price point at Sweet Life often gives people the impression that it is only a destination for special occasions. Mrs. Guerin admits that designing a three-course menu to sell for $45 was a challenge, but she hopes the promotion will draw in enough business to make up for the price reduction. “The objective isn’t to reduce portions down to nothing, it’s to offer the customers an experience that they would have here on any regular night,” she said.

“Restaurants are part of that Vineyard magic package,” said Susan Goldstein, proprietor of the Mansion House and Zephrus in Vineyard Haven. “Everyone should be able to taste and to dip into, in an affordable way, everything that the Vineyard has to offer . . . I really like the idea of that kind of collaborative spirit.”

Other participating restaurants include Atlantic, Atria, Chesca’s, The Grill on Main, l’etoile, Wharf Pub, Seafood Shanty and David Ryan’s in Edgartown; Black Dog Tavern, Blue Canoe, Water Street and Nicky’s Italian Cafe in Vineyard Haven; Mediterranean, Offshore Ale, Sharky’s Cantina, Smoke n’ Bones and The Lookout in Oak Bluffs, the Lambert’s Cove Inn in West Tisbury, and Chilmark Tavern in Chilmark.

Ms. Bellante-Holand likened the week to a great big dinner party, and said she plans to go out with a big group of friends. “We’ve already started to put together our list of where we are going. After all this rain, I’m definitely ready for a party,” she said.

For a list of participating restaurants and menus, visit the Web site marthasvineyardrestaurantweek.com. Restaurants interested in participating should contact Dawn Bellante-Holand at 508-696-7961.