In this paper, equations calculating lift force of a rigid circular cylinder at lock-in in uniform flow are deduced in detail. Besides, equations calculating the lift force on a long flexible circular cylinder at lock-in are deduced based on mode analysis of a multi-degree freedom system. The simplified forms of these equations are also given. Furthermore, an approximate method to predict the forces and response of rigid circular cylinders and long flexible circular cylinders at lock-in is introduced in the case of low mass-damping ratio. A method to eliminate one deficiency of these equations is introduced. Comparison with experimental results shows the effectiveness of this approximate method.