We study the segregation process of a granular mixture of discs on an horizontally oscillating tray by realistic molecular dynamics simulations. As found in the experiments, we observe the initially disordered mixture to segregate via the formation of stripes perpendicular to the driving direction. The segregation process turns out to be the result of a dynamical instability very similar to the Kelvin–Helmholtz instability observed in fluid mechanics, and it is not due to the depletion potential, i.e., to the effective potential existing between two big particles in a bath of smaller ones, but rather to a dynamical process whose nature is discussed.