The recovery of two rare earth metal ions (REs) [Y3+ and La3+, belonging to heavy and light REs, respectively] was studied using functionalized poly(glycidylmethacrylate) adsorbent (F-PGMA) modified with polyaminophosphonic acid moieties. By using CHNP/O, BET, SEM, pH-titration, XRD, XPS, and FTIR analysis techniques, the structure of the synthesized adsorbent was clarified. The adsorption properties toward Y3+ and La3+ were compared and the interaction behaviors were explained with XPS and FTIR analysis. The saturation adsorption capacities (in mmol.g-1) have the following order: La3+ (0.795) > Y3+ (0.744) at optimal pH0 5.0. The adsorption was endothermic with fast kinetics (180/240 min) and the adsorption half-time (t1/2) 16.2 and 29.3 min for La3+ and Y3+, respectively. Langmuir and pseudo-second-order equations (PSO) fit well experimental data. Also, the possible complexes structures were explained. According to the adsorption test in bi-system solution, KSC(La3+/Y3+) was about 1.7. Desorption and adsorbent recycling were successfully achieved using HNO3 solution (0.5 M). The F-PGMA shows high durability over six cycles with desorption efficiency >93% and >95% for La3+ and Y3+, respectively. The adsorption process was described quantitatively using novel three-dimensional (3D) nonlinear mathematical model. The advanced theoretical studies were achieved by the MATLAB software, utilizing a variety of models. The data were then fitted using a successive approximations approach with many trails. The Floatotherm included Van't Hoff parameters model was revels the endothermic and spontaneous behaviors of the adsorption process. Vermeulen model of the binary system indicates that, the adsorption process was achieved with a synergism behavior and the Y element exhibited more competition than La.