The magnetic properties of Mn monolayer on Ag (111) surface have been studied, using the first-principle plane-wave implementation of the density-functional theory (DFT). Several collinear and non-collinear magnetic configurations have been considered including the effects of different stacking sequences for the surface termination. We compare our results with recent experimental data of Gao et al. [C. L. Gao, W. Wulfhekel and J. Kirschner, Phys. Rev. Lett. 101, 267205 (2008)]. Our simulations reveal that the lowest energy state is antiferromagnetic, and corresponds to an out-of-plane collinear antiferromagnetic state, when we take into account the spin-orbit interactions while the 120° antiferromagnetic Néel structures has an excess energy of 56.06 meV/Mn. The magnetic anisotropy energy found between the antiferromagnetic out-of-plane and in-plane structures is of 2.65 meV. These findings are in agreement …