The physical processes taking place during AFM imaging of soft biological membranes are investigated. A particular emphasis is placed on understanding of hydrodynamics effects in the fluid inside and outside of the cell associated with elastic deformation of the membrane in response to AFM tapping action for the entire probing cycle. For the first time, it is theoretically shown that "hysteresis" in the membrane deformation versus tip-sample separation curve is due to strong coupling of fluid motion and kinematics of the membrane bending for the noncontact mode of measurements in liquid environment. The effects of the AFM tip opening angle and the membrane elasticity constants such as bending rigidity and spontaneous curvature are investigated in detail to establish the structure of the flow field and dynamics of the membrane evolution, leading to theoretical interpretation of AFM imaging experiments.