By numerically evaluating the beam-shape and the Mie coefficients for an incident Bessel Beam, we show some preliminary results in trapping both conventional and metamaterial particles in optical tweezers, by calculating the gradient forces exerted on them. Some comparisons between scattering phenomena and the ray optics regime for optical trapping are made. We conclude that, contrary to the conventional case of positive refractive index, the gradient forces acting on a metamaterial particle may not invert when the relative refractive index n goes from |n| > 1 to |n| < 1. ©2009IEEE.