A numerical research on nonlinear time-dependent fields of velocity and pressure in viscous incompressible fluid near an oscillating solid infinitely of the length limited in the direction of oscillation thin plate was performed. The limitation of the plate size along the direction of its oscillation leads to nonlinearity of the problem even when oscillation amplitude of the plate surface is small. The fields of velocity and pressure with big oscillation amplitudes of the plate surface were studied. The explanation of the displacement flows appearance while oscillation of an infinitely thin plate of limited length was given.