This paper is devoted to the design and analysis of the gastroenterology (GI) clinic in the Digestive Health Center (DHC) of University of Wisconsin Health. The DHC will consolidate several existing clinic and endoscopy locations into a single center. First, the work flow at a current GI clinic is studied. A Markov chain model is developed and then extended to non-Markovian case to evaluate patient average length of stay and staff utilization. The model is validated by the data observed in the clinic. It is shown that the model can provide accurate estimation of system performance. Then, using such a model, design options of the new GI clinic in the DHC are studied. To investigate the impact of different system configurations, what-if analyses are carried out and different patient check-out processes are investigated. Finally, recommendations for enhancing service at the new GI clinic are proposed to the DHC leadership.