Empathy is commonly defined as the capacity to stand in another's shoes and can be generally divided into two major components: affective and cognitive empathy. The role and importance of empathy in clinical practice have been widely discussed in the research community at large and there have been numerous initiatives to train physicians and nurses in empathic communication. Qualitative and quantitative investigations of clinical practice settings involving empathy have primarily focused on patient experience, yet little has been done on the quantitative analysis and modeling of clinical empathy themselves. In this paper, we address two important aspects of clinical empathy modeling: the design and implementation of a new annotation protocol, and an automatic classification system trained on a new corpus of narrative essays written by pre-med students. To develop the annotation protocol, we built MedicalCare, a corpus of essays simulating a doctor's delivery of bad news to a hypothetical patient. We compared our results with state-of-the-art research on empathy prediction using self-rated empathy scores. Our research suggests that the classification system we built is effective in modeling clinical empathy and that our annotation protocol is more reliable when compared with self-assessment approaches to empathy prediction.