||We present a 2D incompressible Navier-Stokes numerical simulation of a virtual model of an elliptic, or flat plate, foil in hovering flight configuration. Computations obtained with a general purpose solver were validated against reference data on forward flapping flight, normal or dragonfly hovering. The moving mesh technique allows airfoil translation and angular mesh movement accompaining the airfoil stroke motion. Close to the ground the mesh deforms to occupy the narrow computational domain formed between the airfoil and the ground. Computations have been carried out for some parameters, including the distances h between the foil center and the surface, h/c=¥, 1.5 and 1.0, for chord Reynolds numbers of 157, 1570 and 3140. The combination of the selected parameters showed force reduction and force recovery to the free dragonfly mode. During the first stroke, lift is dominated by leading edge vortex and wake capture. With the number of strokes increasing, the interactions between the airfoil and the regions related to the previous stroke vortices and the vortices emanating from the boundary layer on ground growth, and the drag and lift temporal evolution do not show a periodic behavior with the stroke motion.