A method of making stretchable absorbent articles includes the steps of providing a continuous substrate layer, providing one or more streams of adhesive fibers and superabsorbent particles, shaping the one or more streams of adhesive fibers and superabsorbent particles, depositing the adhesive fibers and superabsorbent particles on the substrate layer to form a plurality of shaped absorbent cores bound to the substrate layer, and separating the absorbent cores from each other. The absorbent cores thus formed do not prevent stretching of the substrate layer. The combination of absorbent core and substrate layer can be used in a wide variety of personal care absorbent articles and medical absorbent articles.