Milling process is a multi-dimensional cutting process accompanied by chatter vibrations because of material removal discontinuity. Also, chatter phenomenon has a great impact on final milled products quality. In this paper, an adequate criterion derived from mathematical literature is used to predict stability of multi-dimensional chatter milling. For that, firstly, the chatter milling system is represented by a system of three Degrees Of Freedom (DOF) and its dynamics is modeled by a system of Retarded Differential Equations (RDEs). Afterward, stability in Lyapunov sense is computed on the basis of the quasi-polynomial characteristic function in frequency domain. Finally, this method is used to predict stability of chatter milling process under different machining conditions and the output related to each case is verified by resolving the system of RDEs and visualizing the displacements in time domain using Matlab software.