Nanostructures made of metallic materials support collective oscillations of their conduction electrons, commonly known as surface plasmons. These modes, whose characteristics are determined by the material and morphology of the nanostructure, couple strongly to light and confine it into subwavelength volumes. Of particular interest are metallic nanostructures for which the size along one dimension approaches the nanometer or even the subnanometer scale, since such morphologies can lead to stronger light–matter interactions and higher degrees of confinement than regular three‐dimensional nanostructures. Here, the plasmonic response of metallic nanodisks of varying thicknesses and aspect ratios is investigated under far‐ and near‐field excitation conditions. It is found that, for far‐field excitation, the strength of the plasmonic response of the nanodisk increases with its thickness, as expected from the increase in the number of conduction electrons in the system. However, for near‐field excitation, the plasmonic response becomes stronger as the thickness of the nanodisk is reduced. This behavior is attributed to the higher efficiency with which a near‐field source couples to the plasmons supported by thinner nanodisks. The results of this work advance the understanding of the plasmonic response of thin metallic nanostructures, thus increasing their potential for the development of novel applications.