  Experimental data on $^{96}$Zr indicate coexisting spherical and deformed
structures with small mixing amplitudes. We investigate the properties of the
low-lying collective states of $^{96}$Zr based on the collective quadrupole
Bohr Hamiltonian. The $\beta$-dependent collective potential having two minima
-- spherical and deformed, is fixed so to describe experimental data in the
best way.Good agreement with the experimental data on the excitation energies,
$B(E2)$ and $B(M1)$ reduced transition probabilities is obtained. It is shown
that the low-energy structure of $^{96}$Zr can be reproduced in a satisfactory
way in the geometrical model with a potential function supporting shape
coexistence. However, the excitation energy of the $2^+_2$ state can be
reproduced only if the rotation inertia coefficient is taken five times smaller
then the vibrational one in the region of the deformed well. It is shown also
that shell effects are important for the description of the $B(M1;2^+_2
\rightarrow 2^+_1)$ value. An indication on the influence of the pairing
vibrational mode on the $\rho^2 (0^+_2 \rightarrow 0^+_1)$ value is obtained.
