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Electromagnetically induced transparencies (EITs) in metallic nanostructures and metamaterials have attracted increasing attentions in recent years, because of many applications such as optical sensing. In this work, we study theoretically the classical analogy of double EITs in a peridic array of metal nanodisks on a dielectric film. It is found that the double EITs arise from the interactions between the localized surface plasmons (LSPs) of metal nanodisks and the waveguide modes within dielectric film. The resonance positions of double EITs can be predicted analytically by the well-known waveguide theory, and can be also largely tuned by varying the array period of metal nanodisks or the thickness of dielectric film. With the help of theoretical model of Fano interference, the EITs profile is approximately reproduced. The double EITs may hold potential in refractive index sensing.