  Experimental data on $^{96}$Zr indicate coexisting spherical and deformed
structures with small mixing amplitudes. Several collective low-lying states
and E2 and M1 transitions are observed for this nucleus. The
quadrupole-collective Bohr Hamiltonian depending on both $\beta$ and $\gamma$
shape variables with a potential having spherical and deformed minima, is
applied consideration of these data. The relative depth of two minima, height
and width of the barrier, rigidity of the potential near both minima are
determined so as to achieve a satisfactory description of the observed
properties of the low-lying collective quadrupole states of $^{96}$Zr. Good
agreement with the experimental data on the excitation energies, $B(E2)$ and
$B(M1; 2^+_2\rightarrow 2^+_1)$ reduced transition probabilities is obtained.
It is shown that the low-energy structure of $^{96}$Zr can be described in a
satisfactory way within the Geometrical Collective Model with a potential
function supporting shape coexistence without other restrictions of its shape.
However, the excitation energy of the $2^+_2$ state can be reproduced only if
the rotation inertia coefficient is taken by four times smaller than the
vibrational one in the region of the deformed well. It is shown also that shell
effects are important for the description of the $B(M1; 2^+_2 \rightarrow
2^+_1)$ and $B(M1; 3^+_1 \rightarrow 2^+_1)$ transition probabilities. An
indication for the influence of the pairing vibrational mode on the $0^+_2
\rightarrow 0^+_1$ transition is confirmed in agreement with the previous
result.
