A method for producing thin MEMS chips on SOI substrate including: providing an SOI substrate having a silicon layer on a front side and having an oxide intermediate layer, producing a layer structure on the front side of the SOI substrate and producing a MEMS structure from this layer structure, capping the MEMS structure and producing a cavity, and etching a back side of the SOI substrate down to the oxide intermediate layer. Also described is a micromechanical component having a substrate, a MEMS layer structure having a MEMS structure in a cavity and a cap element, the MEMS structure and its cavity being enclosed by the substrate underneath and the cap element above, the substrate being made of polycrystalline silicon.