Using the analytic modified embedded atom method (MEAM), the embedding, potential and modifying functions for the Mg and rare earth (RE) metals (RE = Sc, Y, Pr, Nd, Gd, Tb, Dy, Ho and Er) are presented. The thermodynamic properties, such as the dilute-limit heats of solution, enthalpies of formation of disordered solid solutions and intermetallic compounds, for the binary Mg-RE alloys are calculated. The obtained results are in good agreement with the available experimental data and with the results calculated using Miedema theory. The calculations of the enthalpies of formation of Mg3RE, Mg2RE, MgRE, MgRE2and MgRE3with various ordered structures (DO3, DO19, L12, C15, MoPt2, B2, W1 and L10) indicate that the trends in the structural stability can be interpreted directly in terms of the formation energy. Moreover, the lattice constants and volume contractions of alloys with various compositions are determined based on the relation between the formation energy and the interatomic distance. The correlation between the enthalpy of formation and volume contraction for intermetallic compounds is discussed.