The elastic compliance of a work-piece under machining forces during machining operation and its subsequent spring back causes dimensional error. This phenomenon is more critical in turning process especially when long work-pieces are machined between chuck and center or between centers. Ultrasonic vibration assisted turning (UAT) where the cutting tool is put into an ultrasonicfrequency vibration during the ordinary cutting process leads to considerable improvement of the machined work-piece including increase in the dimensional accuracy. This is partly attributable to the noticeable decrease of the machining force in UAT compared with those occurring in conventional turning (CT). It is noteworthy that UAT is regarded as an advanced machining technique which is especially suitable for machining of brittle and hard-to-cut materials such as glass, ceramics and super alloys. In the present study, the diametrical error due to the spring back of work-piece being machined between chuck and center in turning operation is first analyzed. A model is then presented for prediction of this error in UAT by statistical analysis of extant experimental results. All influencing parameters are thus taken into consideration when deriving the predicting model. This model is verified by FEM simulation.