Foamed plastic structures that include one or more foamed plastic bodies containing a polymer matrix that includes one or more polymers formed by polymerizing a monomer mixture formed by polymerizing a monomer mixture containing vinyl aromatic monomers using a polymerization initiator having a structure corresponding to: R(Y).sub.n where R is a C.sub.2 to C.sub.32 linear, branched, and/or cyclic aliphatic and/or aromatic group that can also include one or more atoms selected from oxygen, nitrogen, halides, silicon and sulfur, Y is a group that can generate a free radical capable of initiating polymerization of the monomers in the monomer mixture; and n is from 2 to 6. The structures formed can include, as non-limiting examples, pallets, containers, stackable containers, produce boxes, seafood shipping containers, geofoam blocks, and insulated concrete forms.