Multiferroicity can be induced in strontium titanate by applying biaxial strain, resulting in the coexistence of both ferroelectric and antiferrodistortive domains. The magnitude and sign of the strain imposed on the lattice by design can be used to tune the phase transitions and interactions between these two phenomena. Using optical second harmonic generation, we report a transition from centrosymmetric 4/mmm phase to ferroelectric mm2, followed by an antiferrodistortive transition to a coupled ferroelastic-ferroelectric mm2 phase in a strontium titanate thin film strained in biaxial tension by 0.94%. The results agree well with theoretical first principles and phase-field predictions. Direct imaging of domains arising from the ferroelectric phase transition, and its switching under electric fields is demonstrated using piezoelectric force microscopy. Nonlinear optics combined with phase-field modeling is used to show that the dominant multiferroic domain switching mechanism is through coupled 90• ferroelectric-ferroelastic domain wall motion. More broadly, these studies of coexisting ferroelectric (polar) and antiferrodistortive rotation (axial) phenomena could have relevance to multiferroics with coexisting ferroelectric (polar) and magnetic (axial) phenomena.PACS numbers: 77.84. Dy, 77.80.Dj, 77.80.Fm, 42.70.Mp Multiferroic materials with multiple order parameters such as polarization, magnetization, and spontaneous strain lead to the coexistence of two or more of the primary ferroic properties. As a consequence, multiferroics are attracting significant interest due to the possibility of a rich array of coupled phenomena such as ferroelasticelectric-magnetic, piezo-electric-magnetic, and electromagneto-optic effects [1,2,3,4,5,6,7,8]. At first glance, strontium titanate would appear an unlikely candidate for a multiferoic. Bulk SrTiO 3 is a cubic (m3m) centrosymmetric perovskite at room temperature; it undergoes a nonpolar antiferrodistortive (AFD) phase transformation to a tetragonal point group 4/mmm at ∼105 K, and exhibits indications of a frustrated ferroelectric (FE) transition at ∼20 K, which it never completes [9]. First principles calculations [10] and thermodynamic analysis [11,12] have suggested however, that external strain can induce ferroelectricity. This prediction has been experimentally confirmed recently in a SrTiO 3 thin film strained in biaxial tension [13]. A number of fundamental issues, however, remain to be addressed. No direct imaging of ferroelectric domains or its switching dynamics has been reported in this material. The multiferroic nature of strained strontium titanate, i.e., the coexistence of ferroelectric and ferroelastic domains has not received much attention, though it is unique in many respects. It is induced by external strain. Further, unlike other ferroelectric-ferroelastics such as BaTiO 3 and PbTiO 3 * In review in Physical Review Letters which have a primary order parameter in polarization and secondary order parameter in strain, two independent primary order par...