A method of producing a composite elastic material comprises stretching an elastic web to elongate it, for example, elongating a nonwoven web of meltblown elastomeric fibers, and bonding the elongated web to at least one gatherable web, such as a spunbonded polyester fiber material, under conditions which soften at least a portion of the elastic web to form the bonded composite web of elastic material. The composite material is relaxed immediately after the bonding to prevent the elastic web from losing its ability to contract from the stretched dimensions which it assumed during the bonding step. Such immediate relaxation of the composite material after the bonding step results in the elastic web retaining its ability to contract so that, upon termination of the elongating force, the elastic web contracts to form gathers in the gatherable web. The bonding may be effectuated by pattern embossing overlaid elastic and gatherable webs with at least portions of the elastic web heated to at least its softening temperature. The resultant composite elastic material comprises a coherent elastic web which is bonded to at least one coherent gatherable web whereby the gatherable web is extensible and contractible with the elastic web upon stretching and relaxing of the composite material.