A review of literature relating Human Resources (HR) and Lean Manufacturing (LM) revealed that none of the papers have provided a clear-cut description regarding the roles and responsibilities of the internal and external stakeholders of an organisation while implementing LM. Apart from this, no papers have described a methodology to quantify the roles and responsibilities of HR. Hence, this paper attempts to fill in these gaps by establishing the taxonomy for LM elements by proposing a conceptual framework from the perspective of HR. Finally, a mathematical model based on the Graph Theory (GT) is developed to quantify their roles and responsibilities of various stakeholders of HR in a LM environment. © 2010 Inderscience Enterprises Ltd.