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Experimental data on $^{96}$Zr indicate coexisting spherical and deformedstructures with small mixing amplitudes. Several collective low-lying statesand E2 and M1 transitions are observed for this nucleus. Thequadrupole-collective Bohr Hamiltonian depending on both $\beta$ and $\gamma$shape variables with a potential having spherical and deformed minima, isapplied consideration of these data. The relative depth of two minima, heightand width of the barrier, rigidity of the potential near both minima aredetermined so as to achieve a satisfactory description of the observedproperties of the low-lying collective quadrupole states of $^{96}$Zr. Goodagreement 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 asatisfactory way within the Geometrical Collective Model with a potentialfunction supporting shape coexistence without other restrictions of its shape.However, the excitation energy of the $2^+_2$ state can be reproduced only ifthe rotation inertia coefficient is taken by four times smaller than thevibrational one in the region of the deformed well. It is shown also that shelleffects are important for the description of the $B(M1; 2^+_2 \rightarrow2^+_1)$ and $B(M1; 3^+_1 \rightarrow 2^+_1)$ transition probabilities. Anindication for the influence of the pairing vibrational mode on the $0^+_2\rightarrow 0^+_1$ transition is confirmed in agreement with the previousresult.

Description of the low-lying collective states of $^{96}$Zr based on the quadrupole-collective Bohr Hamiltonian