Abstract: In recent years, a new high accuracy rheological model-RS model was proposed by Robertson -stiff. Owing to lack of calculating formula, this model has been restricted in application. According to RS constituent equation we derive the velocity of flow, flow rate, pressure loss and the size of unsheared plug-flow as RS fluid flowing in pipe and concentric annulus under axial laminar condition. Through verification, the results show that the formula can be used in predicting.