The COVID-19 pandemic has caused significant social and economic disruption across the globe. Cellular entry of SARS-CoV-2 into the human body is mediated via binding of the Receptor Binding Domain (RBD) on the viral Spike protein (SARS-CoV-2 RBD) to Angiotensin-Converting Enzyme 2 (ACE2) expressed on host cells. Molecules that can disrupt ACE2:RBD interactions are attractive therapeutic candidates to prevent virus entry into human cells. A computational strategy that combines our Peptide Binding Design (PepBD) algorithm with atomistic molecular dynamics simulations was used to design new inhibitory peptide candidates via sequence iteration starting with a 23-mer peptide, referred to as SBP1. SBP1 is derived from a region of the ACE2 Peptidase Domain α1 helix that binds to the SARS-CoV-2 RBD of the initial Wuhan-Hu-1 strain. Three peptides demonstrated a solution-phase RBD-binding dissociation constant in the micromolar range during tryptophan fluorescence quenching experiments, one peptide did not bind, and one was insoluble at micromolar concentrations. However, in competitive ELISA assays, none of these peptides could outcompete ACE2 binding to SARS-CoV-2-RBD up to concentrations of 50 μM, similar to the parent SBP1 peptide which also failed to outcompete ACE2:RBD binding. Molecular dynamics simulations suggest that P4 would have a good binding affinity for the RBD domain of Beta-B.1.351, Gamma-P.1, Kappa-B.1.617.1, Delta-B.1.617.2, and Omicron-B.1.1.529 variants, but not the Alpha variant. Consistent with this, P4 bound Kappa-B.1.617.1 and Delta-B.1.617.2 RBD with micromolar affinity in tryptophan fluorescence quenching experiments. Collectively, these data show that while relatively short unstructured peptides can bind to SARS-CoV-2 RBD with moderate affinity, they are incapable of outcompeting the strong interactions between RBD and ACE2.