Emergency Departments often experience sudden increases in patient visits, referred as surge. Surge brings challenges to setting staffing requirement. Since the patient arrival rate is not constant over time during surge, a network of nonstationary queueing models and time-varying discrete event simulation models have been developed to model the surge in emergency department. For queueing models, to mathematically analyze this time-varying system, many approximation methods that have been proposed in literature are compared in this work in order to identify the best approach for modelling surge. Due to the lack of analytical approaches to evaluate these methods, a validated time-varying simulation model was used as the reference for comparison. In addition, a detailed discrete event simulation model was built and validated with historical data for St. Paul’s hospital in BC, Canada. Both the queueing theory approach and simulation method are studied and their advantages and disadvantages are discussed for modelling surge.