The forces acting on dielectric particles and living cells exposed to alternating and rotating fields generated by three-dimensional multi-electrode arrangements are investigated. Numerical procedures are described for the calculation of the electric field distribution and forces. The physical treatment considers electrodes of any shape and dielectric particles of complex structure. Particle and cell trapping are based on negative dielectrophoretic forces produced by high-frequency a.c. or rotating electric fields up to 400 MHz. Various multi-electrode systems were realised in commercially fabricated microelectrode systems, and tested for their ability to move and assemble microparticles or living cells without contact with the electrodes. The field distribution and accuracy of phase-controlled power application was tested using individual artificial particles trapped in the electric field cage. Position and trajectories of particle motion were measured. The paper gives an overview of electrode and field cage design in the microscale range.