Sorption of the 14 rare earth elements (REE) by basaltic rock is investigated as a function of pH, ionic strength and aqueous REE concentrations. The rock sample, originating from a terrestrial basalt flow (Rio Grande do Sul State, Brazil), is composed of plagioclase, pyroxene and cryptocrystalline phases. Small amounts of clay minerals are present, due to rock weathering. Batch sorption experiments are carried out under controlled temperature conditions of 20 °C with the <125 μm fraction of the ground rock in solutions of 0.025 M and 0.5 M NaCl and at pH ranging from 2.7 to 8. All 14 REEs are investigated simultaneously with initial concentrations varying from 10−7 to 10−4 mol/L. Some experiments are repeated with only europium present to evaluate possible competitive effects between REE. Experimental results show the preferential retention of the heavy REEs at high ionic strength and circumneutral pH conditions. Moreover, results show that REE sorption increases strongly with decreasing ionic strength, indicating two types of sorption sites: exchange and specific sites. Sorption data are described by a Generalised Composite (GC) non-electrostatic model: two kinds of surface reactions are treated, i.e. cation exchange at >XNa sites, and surface complexation at >SOH sites. Total site density (>XNa + >SOH) is determined by measuring the cation exchange capacity (CEC = 52 μmol/m2). Specific concentrations of exchange sites and complexation sites are determined by fitting the Langmuir equation to sorption isotherms of REE and phosphate ions. Site densities of 22 ± 5 and 30 ± 5 μmol/m2 are obtained for [>XNa] and [>SOH], respectively. The entire set of REE experimental data is modeled using a single exchange constant (log Kex = 9.7) and a surface complexation constant that progressively increases from log K = −1.15 for La(III) to −0.4 for Lu(III).The model proves to be fairly robust in describing other aluminosilicate systems. Maintaining the same set of sorption constants and only adjusting the site densities, we obtain good agreement with the literature data on REE/kaolinite and REE/smectite sorption. The Generalised Composite non-electrostatic model appears as an easy and efficient tool for describing sorption by complex aluminosilicate mineral assemblages.