<p>Methanesulfonic acid (MSA) is a strong organic acid that is being regarded as an eco-friendly alternative to conventional mineral acids in the domain of hydrometallurgy. In the present work, the application of MSA for the extraction of Rare Earth Elements (REEs) from phosphogypsum (PG), a by-product of the phosphoric acid manufacturing process, is demonstrated using a design of experiments (DOE) approach. The different leaching parameters (temperature, acid concentration, solid-to-liquid ratio, and process duration) and their interaction terms have been studied. X-Ray diffraction analysis of the PG sample indicated gypsum (CaSO₄.2H₂O) as the major phase. The scanning electron microscopy–energy dispersive spectroscopy (EDS) and scanning transmission electron microscopy-EDS analysis indicated that the REEs in the sample are present partially as a part of the gypsum matrix and the rest as constituents of associated minerals. Multivariate linear regression is used to fit the leaching efficiencies obtained from the DOE study, with the corresponding leaching parameters in a first-order equation, containing the individual parameters and the interaction terms. The highest leaching efficiency (of total REEs) of 81% is achieved under conditions of: temperature: 80&#xa0;℃, acid concentration: 2&#xa0;M, duration: 60&#xa0;min, and solid-to-liquid ratio: 1/12. The statistical analysis revealed that temperature, acid concentration and the interaction of temperature and solid-to-liquid ratio are statistically significant factors controlling the leaching of REEs from PG with methanesulfonic acid. Following a similar methodology, a separate model is also proposed for the leaching of neodymium (Nd) only, since it is an element of interest to industries and policymakers for its critical applications.</p> Graphical Abstract <p></p>