We report first-principles calculations that clarify stability and electronic structures of silicene on Ag(111) surfaces. We find that several stable structures exist for silicene/Ag(111), exhibiting a variety of images of scanning tunneling microscopy. We also find that Dirac electrons are absent near Fermi level in all the stable structures due to buckling of the Si monolayer and mixing between Si and Ag orbitals. This is the first theoretical investigation that clarify the absence of Dirac electrons in silicene due to the strong interaction with substrates. We instead propose that either BN substrate or hydrogen-processed Si surface is a good candidate to preserve Dirac electrons in silicene.