The purpose of this research is to discuss the machining stability in of the up and down milling of three milling systems: 1) the feed-direction one-dimension, 2) the normal-to-feed-direction one-dimension and 3) the symmetric two-dimension milling systems. A simplified model with time-invariant parameters is adopted to simulate the milling process. In this model, the elementary cutting function, which represents the trajectory of cutting force for a certain local cutting edge, plays an important role in affecting machining stability of the different cutting configurations. This paper presents an in-depth discussion on the effects of cutting configurations and radial depth of cut on the elementary cutting function, and also on the stability lobes. It is found that the elementary cutting function of one-dimension milling system is a real number, as well as its positive and negative values will lead to totally different chatter features. Most technical literatures focus on the chatter features of positive elementary cutting function, while this research discuss that of both positive and negative ones. On the other hand, for the two-dimension milling system, its machining stability found to be dominated by the eigenvalues of the elementary cutting function matrix. The comparison of machining stability in up and down milling is then analyzed and three conclusions are drawn in this research. Firstly, the feed-direction one-dimension milling system has better machining stability in up milling. Secondly, the normal-to-feed-direction one-dimension milling system has better machining stability in down milling. Thirdly, up and down milling both show the same machining stability in the symmetric two-dimension milling system.