In the first part of this talk, we discuss a study of the instability of the one-dimensional concentration waves in fluidised beds to transverse disturbances, leading to gravitational overturning. We will start by presenting the governing equations of this flow and the modelling assumptions. We use a simplified two-fluid model and perform linear stability analyses and numerical simulations. We show that fluidised beds are gravitationally unstable to long wavelength transversal modes. Then on the second part, we will show some preliminary results on the study instabilities in fluidised beds using a hybrid method in which the motion of the particles is solved explicitly, using a molecular dynamics technique, and the fluid flow is solved using the standard averaged balance equations, in an intermediate length scale. This approach is computationally much cheaper than solving the actual flow and its interaction with the particles, and does not need the standard closure equations necessary for a continuum description of the particles. Time allowing, in a third part of the talk, we will discuss some problems on granular materials and on the dynamical interaction of magnetic particles.