Non-dispersive solvent extraction (NDSX) in a micro-contactor eliminates the need of phase separator. Thus, NDSX is an approach to achieve intensification of solvent extraction process. The interface between the two phases which flow counter-currently is stabilized by metallic membrane (stainless steel mesh). However, the use of counter-current flow puts hydrodynamic limitations on stability of the interface and hence on the operation of the contactor. In this study, a theoretical model to estimate the maximum stability length and corresponding extraction is reported and validated with the experimental data of nitric acid extraction using 30% (v/v) TBP in dodecane as the solvent. The model is further used to perform parametric analysis to understand the effect of various parameters on maximum stability length and corresponding extraction. The model is also used for assessing feasibility of using metallic membrane-based counter-current micro-contactor for non-dispersive solvent extraction of uranium from nitric acid medium.