The flow direction of a no-free chip has a vital influence on chip control and the machined surface's integrity. In order to establish an accurate prediction model of chip flow direction, a new analytical model considering the effect of workpiece materials and tool nose radius on chip flow direction is proposed for cylindrical turning. The rounded edge engaged in cutting is segmented into many oblique cutting units to consider the effect of the nose radius on the chip flow, whose thermomechanical process of chip formation is characterized by the unequal division shear zone method. The mutual action forces of each discrete chip are calculated to determine the resultant chip flow direction, and the interaction between the constrained chip units is comprehensively considered as non-free chip flow. Simultaneously, the influences of material constitutive and cutting parameters on the flow direction of discrete chip and resultant chip are analyzed by thermomechanical coupling method. The conducted mechanism of the nose radius and the main cutting edge angle on unconstrained and constrained chips is studied. The predicted results of chip flow direction were validated with experimental values and Colewell's model, and the FE simulation was also used to compare with the proposed model, interesting agreement was found.