Food containers formed of sheet plastic are latchably stackable on one another. Each container has base (14) and lid (16) elements, with one of them having an outer rim part with a pair of long handle sections (80, 82) that can be pivoted up to form a handle assembly for carrying the container. The sections that form handles are formed in the lid element (16) rather than in the base element (14), so a person does not have to contend with long bouncing sections if the person eats a meal out of the base. One of the elements has vertically undercut grooves (50) and the other element has horizontal projections (52) that slide into and along the grooves. The grooved element has vertical passages (120) along which the projections can move vertically until they can slide into and along the grooves.