  The two neutrino positron double beta decay of $^{106}$Cd for 0$^{+} \to $
0$^{+}$ transition has been studied in the Hartree-Fock-Bogoliubov model in
conjunction with the summation method. In the first step, the reliability of
the intrinsic wave functions of $^{106}$Cd and $^{106}$Pd nuclei has been
tested by comparing the theoretically calculated results for yrast spectra,
reduced $B(E2$:$0^{+}\to 2^{+})$ transition probabilities, quadrupole moments
$Q(2^{+})$ and gyromagnetic factors $g(2^{+})$ with the available experimental
data. In the second step, the nuclear transition matrix element $M_{2\nu}$ and
the half-life $T_{1/2}^{2\nu}$ for 0$^{+}\to$ 0$^{+}$ transition have been
calculated with these wave functions. Moreover, we have studied the effect of
deformation on nuclear transition matrix element M$_{2\nu}.$
