A new 2-DOFs dynamic turning model including the compliance of workpiece and cutting tool is developed. In past studies, most of them were based on SDOF models and either the workpiece or tool was simplified as rigid one. Meanwhile, traditional regenerative chatter models focus mainly on cross cutting which was particularly prone to chatter. It is evident that such models cannot descript cutting system comprehensively. In order to tackle this problem, we introduce the overlap factor making the new model also suitable for length-wise cutting. Stability was analyzed after performing the Laplace transformation, correlation between critical chip width and spindle speed was derived. Simulation suggests that the new model has a larger critical chip width which complies with practical situation.