The extraction of rare earth elements from apatite concentrate of Chadormalu plant of Iran was studied with the dissolution of ore in nitric acid. The parameters of acidity: 60%, solid to liquid ratio: 30%, leaching time: 30 minute, agitation rate: 200 rpm, temperature: 60 °C and particle size (d₈₀): 50 microns were determined as the optimum operational conditions. The recoveries of lanthanum, cerium, neodymium and yttrium were achieved at 74, 59, 72 and 73%, respectively, in the optimized conditions. Multivariable regression was used to predict La, Ce, Nd, Y and total REEs (Y+Nd+Ce+La) leaching recoveries, using experimental data from laboratory studies. It was achieved quite satisfactory correlations of 0.93, 0.98, 0.99, 0.97 and 0.99 for the prediction of Y, Nd, Ce, La and total REEs recoveries, respectively. It was shown that the proposed equations accurately reproduce the effects of operational variables on the different REEs recoveries, and can be used to optimize the REEs leaching plant.