Abstract: An on-genital erection device for inducing and maintaining the human sexuality are proposed. The on-genital erection device includes an essentially cylindrical elastomeric sleeve surrounding the pre-erection penis. The elastomeric sleeve includes self-sealing air-ports for engaging with an air pump thus forming an expandable and suctioning air tight enclosure of the penis causing its erection. The elastomeric wall can be made of a laminate of at least two layers Li, i=1, 2, . . , M. Each Li includes a surface relief pattern forming a surface relief pattern set that in turn defines a plurality of air paths PTj wherein at least one air path PTk is communicatively connected with the penis surface. Thus, after the plurality of air paths PTj get engaged through their respective air-ports with an external multi-port air pumping device, the desired expandable and suctioning enclosure is formed.