A composite core panel is produced by arranging a plurality of foam strips in adjacent relation and advancing the strips with one or two flexible sheets of porous reinforcement material and adhesive between platens to form a panel. The sheet on one side of the strips is folded between adjacent strips to form double wall pleats which may project either partially or fully between the strips and may have folded end portions overlying the other side of the strips. The second sheet may also form double wall pleats between the strips and be connected to the pleats in the first sheet. The core panel may be cut to form reinforced strips which are connected by adhesive in various arrangements to form other core panels. A core panel may also be formed by wrapping each foam strip longitudinally with a strip of reinforcing material and connecting the strips with adhesive.