We report multiple optical trapping of microscopic dielectric particles using diffractive optical elements (DOEs) implemented with a twisted nematic liquid crystal spatial light modulator (SLM). The particles are trapped simultaneously in an array disposed in plane or in volume and the trapping stability is tested by moving the microscope stage. When using a computer controlled SLM the particles can be moved independently by changing the configuration of the diffractive optical element with a maximum refresh rate of 60 Hz. Translation of the particles in x-y-z is demonstrated inside a volume of 8x8x8 μm 3 . Simultaneous rotation of multiple trapped particles along circular trajectories is demonstrated with different angular velocities. In order to evaluate the maximum speed with which a particle can be moved using our set-up, the Stokes drag force is compared with the trapping force. The performance of our multiple trapping technique is compared with other methods reported in literature.