In this study, the role of elastic and interfacial energies in the shape evolution of T₁ precipitates in Al-Cu-Li alloys is investigated using phase-field modeling. We employ a formulation considering the stoichiometric nature of the precipitate phase explicitly, including coupled equation systems for various order parameters. Inputs such as elastic properties are derived from density functional theory calculations, while chemical potentials are obtained from CALPHAD databases. This methodology provides a framework that is consistent with the derived chemical potentials to study the interplay of thermodynamic, kinetic, and elastic effects on T₁ precipitate evolution in Al-Cu-Li alloys. It is shown that diffusion-controlled lengthening and interface-controlled thickening are important mechanisms to describe the growth of T₁ precipitates. Furthermore, the study illustrates that the precipitate shape is significantly influenced by the anisotropy in interfacial energy and linear reaction rate, however, elastic effects are only of secondary importance.