Modification of the plasmonic response of a metal nano-object due to interaction with a substrate is experimentally investigated measuring the quantitative optical extinction spectra of individual nano-objects with various elongated shapes (bipyramids and rods) deposited on a dielectric (silica) or absorbing (carbon) membrane. Apart from the expected dependence of the nanoparticle surface plasmon resonance (SPR) frequency on the nature of the substrate, large substrate and particle shape dependent modifications of its SPR width are demonstrated. These dependencies are ascribed to strong localization of the electromagnetic field associated with the longitudinal SPR of an elongated nano-object around its tips, leading to different interaction with the substrate depending on the particle shape and 3D orientation relative to the substrate. Both parameters have been precisely determined by electron tomography, permitting excellent reproduction of the experimental data. Experiments performed on silver-encapsulated bipyramids, whose shape evolves from a pyramidal one towards a cylindrical one, further confirm this effect.