A tubular core assembly for winding or unwinding of sheet material, such as newsprint or Rotogravure Print, is provided wherein the opposed ends of an elongate cylindrical core are provided with inside diameter-reducing annular end members. The inside diameter-reducing annular end members are mechanically interlocked with a central core body which is preferably formed by multiple wraps of a paperboard material. Mechanical interlocking is accomplished by a plurality of axial grooves in the bodywall of the central core body member and a plurality of axially extending tongue members on the annular end members which are received in the grooves of the central core body member in interlocking relationship therewith. Because of the mechanical interlocking relationship between the inside diameter-reducing annular end members and the central core body member, the inside diameter-reducing annular end members are secured to the central core body member in positive circumferential and axial locking relationship.