An end mill is a tool used on a milling machine. A milling machine is a machine found inrna metal working shop that is used to remove material from a metal block to make it into arnfinished part. And it is one of the tools used on the milling machine to make a particularrntype of cut. Productivity and surface quality in milling processes have direct effects onrncost, production lead time and quality of machined parts.rnChatter vibrations in milling, which develop due to dynamic interactions between therncutting tool and the workpiece, result in reduced productivity and part quality. Machinerntool chatter causes machining instability, surface roughness, and tool wear in metalrncutting processes. The excessive vibrations of the cutter and workpiece result in poorrnsurface finish, dimensional accuracy and may damage the workpiece and machine tool. Inrnaddition to this cutting force produce deformations of the tool and this cause dimensionalrnand form errors on the workpiece.rnIn this research, generalized equations are presented which can be used for predictingrnstatic and dynamic properties of the cutting tool. Milling forces are modeled for givenrncutter geometry, cutting conditions and work material. The static and dynamicrncharacteristics of tool and tool holder can be obtained by using finite element analysisrn(FEA); simplified equations are created to predict deflections of tools for given geometricrnparameters and material properties and also for natural frequencies and mode shapes ofrncutter dynamics. Finite Element Analysis (FEA) results are compared with the resultsrnobtained from analytic equations, Comparison of natural frequencies between carbide andrnHSS end mills. And a simple method to analytically calculate the approximate optimumrndepths of cut and determine the corresponding spindle speeds by creating the stabilityrnlobe diagram. Chatter vibration free spindle speeds and axial depth of cuts can bernselected from stability chats. The characteristics and limitations of the stability loberndiagram are discussed. Case studies are also provided to illustrate the method and verifyrnthe results.