In Japan, plastic food is called "shokuhin sample" (食品サンプル) or "food sample". These samples have existed in Japan since early 20th century—well before World War II. They're a way for restaurants to show off their menu in an easy to understand way and draw in customers.
Shokuhin sample are made from plastic resin; however, some restaurants occasionally leave out actual food for the day if they need to show off a dish and they do not have the fake version.
Typically, fake food is made in Japan, and the fake food manufactures work very closely with the restaurants to reproduce the food in plastic form that is both appetizing and faithful.
Even now, shokuhin sample are such a part of the dining experience in Japan that many people stop in front of glass cases filled with fake food, decide what they want, and then enter the restaurant. Some Japanese even complain about the lack of fake food when dinning abroad—that they don't get to see what they are ordering beforehand!
At the recent Wonder Festival, an event dedicated to plastic figurines, a company called Kodinmari Seisaku Kobo Co. showed off its cell phone straps with fake food trinkets. The fake food straps are not cheap—they run between ¥500 and ¥900 (US$6.40 to $11.50)—but damn, they look good. Good enough to eat.
Have a look at the shokuhin sample straps in the above gallery, courtesy of Akiba Blog.