Sodium-ion batteries have been considered as a promising alternative to Lithium-ion batteries. The cathode material Na_xFePO₄ of sodium-ion batteries shows phase changes during intercalation. In this work, a phase-field model for Na_xFePO₄ is studied for the first time. A coupled phase-field model for the Cahn-Hilliard diffusion equation and finite deformation elasticity is derived. For the mechanical part, two finite deformation elasticity formulations based on elastic Green strain and logarithmic elastic strain, respectively, are introduced and compared. The material parameters for Na_xFePO₄ are determined. We implemented the model in COMSOL Multiphysics^® for a spherically symmetric problem of sodium insertion into a cathodic particle made of Na_xFePO₄. Furthermore, we compare the two cathode materials Na_xFePO₄ and Li_xFePO₄ to each other in terms of phase changes and stresses, and show that the stresses in the cathode material Na_xFePO₄ are larger at the phase segregated state.