Antibody cocktails represent a promising approach to prevent SARS-CoV-2 escape. The determinants for selecting antibody combinations and the mechanism that antibody cocktails prevent viral escape remain unclear. We compared the critical residues in the receptor-binding domain (RBD) used by multiple neutralizing antibodies and cocktails and identified a combination of two antibodies CoV2-06 and CoV2-14 for preventing viral escape. The two antibodies simultaneously bind to non-overlapping epitopes and independently compete for receptor binding. SARS-CoV-2 rapidly escapes from individual antibodies by generating resistant mutations in vitro, but it doesn't escape from the cocktail due to stronger mutational constraints on RBD-ACE2 interaction and RBD protein folding requirements. We also identified a conserved neutralizing epitope shared between SARS-CoV-2 and SARS-CoV for antibody CoV2-12. Treatments with CoV2-06 and CoV2-14 individually and in combination confer protection in mice. These findings provide insights for rational selection and mechanistic understanding of antibody cocktails as candidates for treating COVID-19.