Abstract: High strength foam-filled materials and methods for their production are disclosed. The high strength materials include cellular structures comprising a plurality of open-ended cells containing polycyanurate foam. The polycyanurate foam-filled cellular structures have synergistically high mechanical properties and improved resistance to moisture. When cyanate ester foamable precursors in the form of tough films are foamed to fill honeycomb cells, the resulting foam-filled honeycomb has uniformly fine foam cell structure and improved bonding between the foam and the honeycomb.