Bubbles columns are widely used as reactors and mass transfer equipment between gas and liquid or solid phases in many areas of the materials-transforming industry. The results known from theoretical and experimental research on flow and mixing of the continuous liquid phase and the relative gas content in bubble columns having diameters up to 0.30 m are presented. Evidence is presented for stable circulatory flow. The field of flow of the two phases is then described with the aid of mass and momentum balance equations. These are solved simultaneously by an analytical and a numerical procedure. Non-linear flow instabilities in the form of several circulation cells are demonstrated as a result of the calculation. In the field of flow of circulation cells the local gas content increases towards the centre of the cell. This is a second-order fluid-dynamic effect which has so far eluded description in two-phase flow using the numerical calculation techniques applied hitherto. The results provide the first possibility of calculating several circulation cells.Theoretical prediction of mixing the continuous phase and the transition from the homogeneous to the heterogeneous flow state in a semi-industrial scale bubble column has thus become possible.