Electrokinesis and dielectrophoresis are important transport phenomena produced by external electric field applied to a microchannel containing a conductive fluid. We developed a CFD code to predict electrokinetic and dielectrophoretic flows in a microchannel with a uniform circular post array. Using the code, we calculated particle velocities driven by electrokinesis and dielectrophoresis, and conducted Monte Carlo simulations to visualize the particle motions. The code was validated by comparing the results with those from previous studies in literature. At a low electric field, electrokinesis and diffusion is the dominant transport mechanism. At a moderate electric field, dielectrophoresis is balanced with electrokinesis and diffusion, resulting in flowing filaments of particles in the microchannels. However, dielectrophoresis overwhelms the flow at a high electric field and traps particles locally. These results provide useful insight for optimizing design parameters of a microfluidic chip for biochemical analysis, especially for development of on-chip sample pretreatment techniques using electrokinetic and dielectrophoretic effects.