An efficient and robust computational method, based on the lattice-Boltzmann method, is presented for analysis of impermeable solid particle(s) suspended in fluid with inertia. In contrast to previous lattice-Boltzmann approaches, the present method can be used for any solid-to-fluid density ratio. The details of the numerical technique and implementation of the boundary conditions are presented. The accuracy and robustness of the method is demonstrated by simulating the flow over a circular cylinder in a two-dimensional channel, a circular cylinder in simple shear flow, sedimentation of a circular cylinder in a two-dimensional channel, and sedimentation of a sphere in a three-dimensional channel. With a solid-to-fluid density ratio close to one, new results from two-dimensional and three-dimensional computational analysis of dynamics of an ellipse and an ellipsoid in a simple shear flow, as well as two-dimensional and three-dimensional results for sedimenting ellipses and prolate spheroids, are presented.