A method of making mutually-reinforced elastic strand/film composites and laminates in which film breakage, strand breakage, and strand alignment problems are minimized or avoided. The method includes casting an elastomeric adhesive film onto a chill roll, extruding elastic strands onto the film while the film is on a chill roll, and stretching the film and strand composite. The stretched composite may be laminated between two facing sheets. Additionally, tension in the composite may be controlled through film composition, strand composition, add-on rate, stretching the composite, and combinations of any of these approaches.