Although many investigations have been performed on localization problems, there still exist some pressing issues. Specifically, it is difficult to show in general well-posed governing equations. Based on the essential features of localization phenomena, a partitioned-modeling approach is proposed here via moving jump conditions for localization problems. By taking the initial point of localization as that point where the type of the governing differential equation changes, i.e. a hyperbolic to an elliptic type for dynamic problems and an elliptic to another elliptic type for static problems, a moving boundary between localized and non-localized deformation zones is defined through jump forms of conservation laws across the boundary. As a result, localization problems might be considered in the same category as shocks in fluids and solidification in heat transfer. To illustrate the proposed procedure, one-dimensional analytical solutions are given with an emphasis on the definition of boundary conditions and the experimental means to determine model parameters associated with localization. Future research is then discussed on an extension to general cases.