Polymer extruded foams that contain cell size enlarging agents are provided. The inventive composition includes a foamable polymer material, at least one blowing agent, and at least one cell size enlarging agent. The blowing agent utilized in the inventive composition is preferably selected such that the composition has a zero ozone depletion and low global warming potential. Examples include any inorganic blowing agents and/or non-hydrogenated chlorofluorocarbons (non-HCFCs). The foamable polymer material is preferably polystyrene. The cell size enlarging agent may be chosen from ethylene vinyl acetate (EVA) and/or ethylene methyl acrylate (EMA). The cell size enlarging agent permits the formation of a foam with large cell sizes that are desirable to achieve a high insulation value and to optimize the physical properties of the foamed product. In addition, the cell size enlarging agent provides an increased cell size to the foamed product without detracting from the physical and thermal properties.