Traveling wave dielectrophoresis provides an interesting method for the controlled movement of microsized particles in suspended mixtures, and as such is a promising tool in microfluidic technology. In this case, the electrostatic force acting on the particles has two components: one due to the spatially varying magnitude of the electric field and the other due to the spatially varying phase. The actual movement of the particle is determined by the combined effect of these two forces and corresponding torques, the viscous drag exerted by the fluid on the particle, and the electrostatic and hydrodynamic particle-particle interactions. This paper presents the first numerical simulations of the motion of particles subjected to all previous forces and torques. Our technique is based on a finite-element scheme in which the particles are moved using a direct simulation scheme respecting the fundamental equations of motion for both the fluid and the solid particles. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the electrostatic forces are computed using the point-dipole approximation. Our simulations show that the particle behavior strongly depends on the mismatch of the dielectric properties between the particles and the fluid, and that the particle-particle interaction force as well as particles rotation speeds play crucial roles in the various regimes.