Motivated by data from an observational, prospective study of 286 patients with non-mild acute pancreatitis (AP) who entered the Intensive Care Unit (ICU) of the Donostia University Hospital between 2001 and mid-2017, we propose a multi-state modeling approach to describe the evolution of patients with acute pancreatitis and at least one organ failure or local complications. An extension of the illness-death model is used allowing to take into account the disease-related events of interest, that is, entry to ICU, discharge from ICU and death due to acute pancreatitis. To this end, the present study describes the course of AP patients and evaluates the effect of different prognostic factors on the multiple disease-related events.