The marker and cell technique for the calculation of time‐dependent incompressible flows is used to study density‐current surges at density ratios between 1.05 and 3.0. The study is performed using the full two‐fluid approach as well as a single‐fluid technique involving solute transport and a Boussinesq approximation to the Navier‐Stokes equation. A comparison of these results indicates that the Boussinesq approximation is reasonably accurate for density ratios less than 1.3. The results of free surface and confined flow calculations are compared and the effects of slope, viscosity, and surface tension on density current flows are examined. Complete descriptions are given for the first time of the techniques used for including solute transport and surface tension in marker and cell calculations, and an analysis of the calculational stability properties of the method is included. The numerical results, which are in good agreement with available experimental measurements, provide information about some previously univestigated aspects of density current flows. Of particular importance here is the variation of the front velocity and height with density ratio, for ratios in the range, 1.2‐3.0. New analytical treatments of the initial current surge, the steady flow, and the effects of viscosity are presented and compared with computed results.