In order to improve their performance, modern organizations are increasingly aware of the need to identify, preserve and manage the crucial knowledge (individual and collective) that are mobilized by their sensitive business processes (SBPs). Thus, it will be necessary to characterize, identify, specify, model and analyze these processes, in order to optimize the activities of identification, localization and management of the knowledge on which it is necessary to capitalize. This paper introduces the problematic of the SBP modeling. Our objective is to provide a conceptual analysis related to the concept of SBP. First of all, we propose a rigorous characterization of SBP (which distinguishes it from classic, structured and conventional BPs). Secondly, we propose a multidimensional classification of SBP modeling aspects and requirements to develop expressive, com-prehensive and rigorous models. Besides, we present an in-depth study of the different modeling approaches and languages, in order to analyze their expressiveness and their ability to perfectly and explicitly represent the new specific requirements of SBP modeling. In this study, we choose the better one positioned nowadays, BPMN 2.0, as the best suited standard for SBP representation. Finally, we propose a semantically rich conceptualization of a SBP organized in a core ontology.