The vibration-induced flow (VIF), in which a mean flow is induced by the interaction between the system vibration and micro-structures, has been studied as a fluid/particle micro-manipulation method that does not require an external pump. While the use of VIF with a wide variety of vibrations is expected to realize sophisticated fluid manipulation, numerical tools to predict these unsteady flows remain difficult. In this study, we have performed a numerical simulation of VIF with different vibrations and micropillar cross-sections. A proposed numerical model, which directly solves the continuity and Navier-Stokes equations in the coordinate system moving with the vibrating micropillar, enables us to avoid the introduction of a moving boundary, and therefore has a significant advantage in numerical stability and accuracy. The immersed boundary technique allows us to embed arbitrary complex micro-structures in the Cartesian computational domain without requiring boundary-fitted meshes for each geometry. The dependencies of characteristics of flow on vibration parameters, such as vibration frequency, amplitude, direction, and the shape of micro-structures, were investigated and compared with the experimental results obtained by the particle image velocimetry (PIV) measurement. Excellent agreement between the numerical and experimental results validates that the present numerical approach can be a powerful tool to design functional VIF systems, such as mixing, particle/cell transport, trapping, and separation.