A composite structural material suitable, for example, as a replacement for wooden boards, is disclosed. It comprises a dimensionally stable core material ensheathed in a dimensionally stable, laminar covering that is adherent to the core material. The laminar covering is comprised of at least one layer of parallel cords (19) bonded to at least one layer of a rigidified web material (10) selected from the group consisting of paper and cloth. Suitable core materials include polyurethane foam (38), optionally filled with particles (32) of granulated rubber, expanded perlite, expandable polymer beads, and/or glass microspheres. The parallel cords (19) preferably are supplied in the form of a strip of polyester cloth, as the warp cords thereof. The web material (10) preferably is kraft paper that is rigidified with an epoxy resin.