This method for producing a non-planar microelectronic component, especially a concave component, involves superposing a layer that contains an active flexible circuit above a cavity shaped according to the desired profile of said component, said cavity being formed in substrate; and applying a pressure difference either side of said layer thereby causing slumping of the flexible circuit into the cavity therefore causing the circuit to assume the shape of the cavity. Superposition of the flexible circuit and the cavity is realized by filling the cavity with a material capable of being selectively removed relative to the substrate and the flexible circuit; then fitting or forming the flexible circuit on the cavity thus filled; then forming at least one feedthrough to access the filled cavity; and by selectively etching the material that fills the cavity via at least one feedthrough in order to remove said material.