A Fano resonance is an asymmetric, resonant scattering phenomenon which occurs in a multitude of fields, such as atomic physics, nuclear physics, nonlinear optics, and nanophotonics. The Fano resonance is a many-particle excitation arising from a single-particle excitation, and occurs due to the interference of a narrow discrete resonance overlapping with a spectrally broad resonance. Multi-element nanoparticles are explored as a means to realize this resonance type, which has a characteristic, steep dispersion useful in sensors, among other devices. A gold dolmen nanostructure consisting of a bright, radiative, dipolar mode coupled with a dark, quadrupolar mode is investigated, which produces the plasmonic analogue of electromagnetically induced transparency through the interference of the bright and dark modes. Additionally, the plasmonic resonance of a metallic nanostructure is extremely sensitive to its local dielectric environment. Vanadium dioxide exhibits a large change in its dielectric function during its metal to insulator phase transition. The combination of the gold dolmen nanostructure with vanadium dioxide produces a tunable Fano resonance. The dimensions of the structure are optimized such that the resonance is near symmetric in shape and located in the near infrared to allow for spectroscopic measurement. The author is unable to obtain experimental results of this hybrid structure, but previous work, combined with simulation data, suggest the proposed structure will exhibit the expected result.