Cancer drugs often fail due to the emergence of clinical resistance. This can manifest through mutations in target proteins that selectively exclude drug binding whilst retaining aberrant function. A priori knowledge of resistance-inducing mutations is therefore important for both drug design and clinical surveillance. Stapled peptides represent a novel class of antagonists capable of inhibiting therapeutically relevant protein-protein interactions. Here, we address the important question of potential resistance to stapled peptide inhibitors. HDM2 is the critical negative regulator of p53, and is often overexpressed in cancers that retain wild-type p53 function. Interrogation of a large collection of randomly mutated HDM2 proteins failed to identify point mutations that could selectively abrogate binding by a stapled peptide inhibitor (PM2). In contrast, the same interrogation methodology has previously uncovered point mutations that selectively inhibit binding by Nutlin, the prototypical small molecule inhibitor of HDM2. Our results demonstrate both the high level of structural p53 mimicry employed by PM2 to engage HDM2, and the potential resilience of stapled peptide antagonists to mutations in target proteins. This inherent feature could reduce clinical resistance should this class of drugs enter the clinic.