Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised. © 2010 Optical Society of America.