The present invention relates to an applicator device for a fluid or paste-like make-up and/or care product across a complex surface of the human body, having an elongated general outer shape axisymmetric about an XX axis; wherein the general outer shape thereof comprises a first rounded volume (1) connected to a second rounded volume (2) by an area (3) with a cross section smaller than the largest cross section of the first and the second volumes: where said device comprises at least one flexible longitudinal arch (10, 11) embedded in at least one point of a core (15) extending along the XX axis, where said at least one arch is suitable for defining with the core a product reservoir having a variable volume, resulting in the pumping of the product.