Antibodies targeting the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) present a promising approach to combat the coronavirus disease 2019 (COVID-19) pandemic; however, concerns remain that mutations can yield antibody resistance. We investigated the development of resistance against four antibodies to the spike protein that potently neutralize SARS-CoV-2, individually as well as when combined into cocktails. These antibodies remain effective against spike variants that have arisen in the human population. However, novel spike mutants rapidly appeared after in vitro passaging in the presence of individual antibodies, resulting in loss of neutralization; such escape also occurred with combinations of antibodies binding diverse but overlapping regions of the spike protein. Escape mutants were not generated after treatment with a noncompeting antibody cocktail.