It is the most humble of vessels for New York City foodstuffs, ubiquitous at Chinese takeout joints and halal street carts. In pre-Starbucks days, coffee came packaged in its puffy embrace.

But the plastic-foam container may soon be going the way of trans fats, 32-ounce Pepsis, and cigarettes in Central Park.

Mayor Michael R. Bloomberg, whose regulatory lance has slain fatty foods, supersize sodas, and smoking in parks, is now targeting plastic foam, the much-derided polymer that environmentalists have long tried to restrict.

On Thursday, Mr. Bloomberg, in his 12th and final State of the City address, will propose a citywide ban on plastic-foam food packaging, including takeout boxes, cups and trays. Public schools would be instructed to remove plastic-foam trays from their cafeterias. Many restaurants and bodegas would be forced to restock.