A method for estimating minimum fluidisation velocities in a well-mixed, bi-disperse fluidised bed of spherical particles is described where a drag model is combined with a particle packing model. The method described does not require empirical input about a specific particle mixture, and so these minimum fluidisation velocities can be estimated over wide ranges of size and density ratios. The treatment is fully non-dimensionalised. It is shown that two minimum fluidisation velocities may be defined for a well mixed bi-disperse bed: the gas speed at which fluidisation initiates determined from considering the bed as a whole, and a higher one corresponding to the balance of forces on an individual particle. The differences between bi- and mono-disperse beds are the change in particle volume fraction owing to packing, the difference in drag around individual particles compared with the average drag, and the action of the hydrostatic pressure gradient. The latter two effects tend to increase the difference between the two limits of minimum fluidisation velocity, while packing decreases it and intensifies the dependence on mass fraction of the minimum fluidisation velocities. The influence of inertia is determined from particle properties through an Archimedes number. Though the inertial effects are not large for a wide range of particles, they can start to dominate other influences on the minimum fluidisation velocities as particle diameter increases. (C) 2019 Elsevier B.V. All rights reserved.