Provided are methods for producing a high strength, but easily deformed, polystyrene foam board that can endure repeated deformations from its original configuration into more complex curved shapes without damaging the board integrity or substantially reducing its structural strength. Also provided are rigid polystyrene foam boards produced by this method that exhibit improved bending and impact resistance while substantially retaining or improving other properties, for example, the thermal dimensional stability and fire resistance, exhibited by corresponding conventional XPS foam boards. The foamable compositions may incorporate one or more of a variety of polymer processing aids for the purpose of altering the performance of the final foam products, thereby allowing the properties of the final foam product to be customized to some degree.