By April 2, 2020, >1 million persons worldwide were infected with severe acute respiratory syndrome coronavirus 2. We used a mathematical model to investigate the effectiveness of social distancing interventions in a mid-sized city. Interventions reduced contacts of adults >60 years of age, adults 20-59 years of age, and children <19 years of age for 6 weeks. Our results suggest interventions started earlier in the epidemic delay the epidemic curve and interventions started later flatten the epidemic curve. We noted that, while social distancing interventions were in place, 20% of new cases and most hospitalizations and deaths were averted, even with modest reductions in contact among adults. However, when interventions ended, the epidemic rebounded. Our models suggest that social distancing can provide crucial time to increase healthcare capacity but must occur in conjunction with testing and contact tracing of all suspected cases to mitigate virus transmission.