The Class I Major Histocompatibility Complex (MHC) is a central protein in immunology as it binds to intracellular peptides and displays them at the cell surface for recognition by T-cells. The structural analysis of bound peptide-MHC complexes (pMHCs) holds the promise of interpretable and general binding prediction (i.e., testing whether a given peptide binds to a given MHC). However, structural analysis is limited in part by the difficulty in modelling pMHCs given the size and flexibility of the peptides that can be presented by MHCs. This article describes APE-Gen (Anchored Peptide-MHC Ensemble Generator), a fast method for generating ensembles of bound pMHC conformations. APE-Gen generates an ensemble of bound conformations by iterated rounds of (i) anchoring the ends of a given peptide near known pockets in the binding site of the MHC, (ii) sampling peptide backbone conformations with loop modelling, and then (iii) performing energy minimization to fix steric clashes, accumulating conformations at each round. APE-Gen takes only minutes on a standard desktop to generate tens of bound conformations, and we show the ability of APE-Gen to sample conformations found in X-ray crystallography even when only sequence information is used as input. APE-Gen has the potential to be useful for its scalability (i.e., modelling thousands of pMHCs or even non-canonical longer peptides) and for its use as a flexible search tool. We demonstrate an example for studying cross-reactivity.