Tkachenko mode is a transverse sound wave in a vortex lattice, which exists in the ground state of a rotating super fluid. It has attracted a lot of attention in vortex dynamics of laboratory and astrophysical super fluids. Observation of this extremely soft mode (of order or less than a few Hz) in laboratory super fluids was very difficult because even slight pinning of vortex ends the Tkachenko wave into a classical inertial wave. This mode is a direct manifestation of the quantum vortices since it depends on the circulation quantum. Tkachenko mode in rotating BEC was investigated numerically with solving the equations of Gross-Pitaevskii theory, but the numerical results do not agree with the experiment. In the present paper, it has been shown that the continuum theory of Tkachenko modes, taking into account density, inhomogenity and compressibility of the condensate, successfully explained the observed experimental data.