The lattice dynamics and energies of phases related to antiferrodistorsive and ferroelectric distortions of bulk crystals and thin films of the SrZrO3 crystal have been calculated within the framework of the ab initio model of an ionic crystal. In the case of a bulk crystal, it has been found that the most energetically favorable phases are related to antiferrodistorsive lattice distortions. Ferroelectricity in the SrZrO3 crystal is suppressed by structural lattice distortions. In the case of thin films, it has been found that the ferroelectric instability is retained after the “rotation” of the oxygen octahedron and the film remains polar both in the case of a free surface and with the inclusion of the SrTiO3 substrate in the calculation. The spontaneous polarization of thin films of different thicknesses in the ferroelectric phase has been calculated.