Rayleigh–Taylor and Kelvin–Helmholtz hydrodynamic instabilities are frequent in many natural and industrial processes, but their numerical simulation is not an easy challenge. This work simulates both instabilities by using a lattice Boltzmann model on multiphase fluids at a liquid-vapour interface, instead of multicomponent systems like the oil–water one. The model, proposed by He, Chen and Zhang (1999) [[1]] was modified to increase the precision by computing the pressure gradients with a higher order, as proposed by McCracken and Abraham (2005) [[2]]. The resulting model correctly simulates both instabilities by using almost the same parameter set. It also reproduces the relation   between the growing rate γ of the Rayleigh–Taylor instability and the relative density difference between the fluids (known as the Atwood number A), but including also deviations observed in experiments at low density differences. The results show that the implemented model is a useful tool for the study of hydrodynamic instabilities, drawing a sharp interface and exhibiting numerical stability for moderately high Reynolds numbers.