This paper contributes to accumulating the knowledge base about prospective elementary school teachers' (PTs') understanding of socio-critical modeling by exploring how PTs make connections to features of mathematical modeling and social justice while posing mathematical problems and reflecting on their problem-posing. We present a conceptual framework for posing problems that connect social justice issues with the features of mathematical modeling. Drawing on the analysis of 36 individual modeling problems generated by the PTs and 36 written reflections PTs completed throughout their problem-posing activity, we illustrate various ways in which PTs connect the multi-faceted features of mathematical modeling (i.e., realistic context, model development, and shareable process) and social justice (i.e., micro -- and macro -- level). The PT-posed problems were categorized as (a) modeling problems presenting micro -- and macro-level social justice issues (27%), (b) modeling problems presenting micro-level social justice issues (22%), (c) contextualized mathematical problems presenting micro -- and macro-level social justice issues (25%), and (d) contextualized mathematical problems presenting micro-level social justice issues (17%). Our work describing the complexity of posing social justice-oriented mathematical modeling (SJMM) problems and articulating decisions PTs make while posing SJMM problems set directions for future efforts and research in teacher preparation.