The present invention relates to absorbent articles and non-absorbent articles which comprise at least one improved double-sided soft and elastic material composite. The composites according to the invention may also be breathable. The composites are produced by incrementally stretching a laminate of an elastic layer between two non-elastic cloth-like layers. The non-elastic cloth-like layers tear during stretching such that the elasticity of the laminate after stretching is substantially the same as the elasticity of the film elastic layer.