Abstract Wettability of a reservoir rock can be altered by changing brine composition, e.g., lowering salinity, adding surfactants. Wettability alteration can mobilize stranded oil and enhance oil recovery. Analytical solution for 1D tertiary low salinity flood shows two saturation shocks one of which is associated with an adverse mobility ratio. The adverse mobility ratio across this shock is not very large, about 1.5 to 3.75 in the cases considered. As the viscosity ratio increases, the width of the oil bank decreases and one of the shocks disappears at high viscosity ratio (>10). The remaining shock at high viscosity ratio is stable. A viscous fingering model is applied to describe the flow instability in relatively homogeneous multi-dimensional porous media. It shows that the viscous fingering is mild and the breakthrough of low salinity injectant is only 11-31% faster than in the 1D flow. If only salts are used for wettability alteration, the capillary pressure is significant and becomes more positive (more water-wet) at low salinity. Positive capillary pressure can provide stability to the flood fronts, unlike surfactant floods where low interfacial tension removes the stabilizing capillary pressure. Low salinity floods are expected to be mildly unstable due to low mobility ratio at adverse saturation shocks and presence of capillary pressure.