High-viscosity elastomeric adhesive compositions including a high softening point tackifier resin in combination with a base polymer can be used to create elastomeric composite laminates having effective adhesion and elastic properties. The elastomeric adhesive compositions suitably have a viscosity between about 100,000 and about 500,000 cps at between about 300 degrees Fahrenheit (149 degrees Celsius) and about 350 degrees Fahrenheit (177 degrees Celsius). Facing layers, such as nonwoven webs, films, elastic strands, fastening material, absorbent material, and the like, can be laminated to one or both surfaces of the elastomeric compositions to form elastomeric composite laminates. A method of making such compositions and laminates involves forming the compositions into elastomeric adhesive films and/or strands.