  The interplay between the band Jahn-Teller distortion and the
superconductivity is studied for the system whose Fermi level lies in two-fold
degenerate band. Assuming that the lattice distortion is coupled to the orbital
electron density and the superconductivity arises due to BCS pairing mechanism
between the electrons, the phase diagram is obtained for different doping with
respect to half-filled band situation. The coexistence phase of
superconductivity and distortion occurs within limited range of doping and the
distortion lowers the superconducting transition temperature $T_c$. In presence
of strong electron-lattice interaction the lattice strain is found to be
maximum at half-filling and superconductivity does not appear for low doping.
The maximum value of $T_c$ obtainable for an optimum doping is limited by the
structural transition temperature $T_s$. The growth of distortion is arrested
with the onset of superconductivity and the distortion is found to disappear at
lower temperature for some hole density. Such arresting of the growth of
distortion at $T_c$ produces discontinuous jump in thermal expansion
coefficient. The variation of strain with temperature as well as with doping,
thermal expansion coefficient, the $T_c$ vs $\delta$ behaviour are in
qualitative agreement with recent experimental observations on interplay of
distortion and superconductivity in cuprates.
