Large scale shell model calculations, with dimensions reaching 10 9 , are carried out to describe the recently observed deformed (ND) and superdeformed (SD) bands based on the first and second excited 0 + states of 40 Ca at 3.35 MeV and 5.21 MeV respectively. A valence space comprising two major oscillator shells, sd and pf , can accommodate most of the relevant degrees of freedom of this problem. The ND band is dominated by configurations with four particles promoted to the pf -shell (4p-4h in short). The SD band by 8p-8h configurations. The ground state of 40 Ca is strongly correlated, but the closed shell still amounts to 65%. The energies of the bands are very well reproduced by the calculations. The out-band transitions connecting the SD band with other states are very small and depend on the details of the mixing among the different np-nh configurations, in spite of that, the calculation describes them reasonably. For the in-band transition probabilities along the SD band, we predict a fairly constant transition quadrupole moment Q0(t)∼170 e fm 2 up to J=10, that decreases toward the higher spins. We submit also that the J=8 states of the deformed and superdeformed band are maximally mixed.