Major histocompatibility complex-I (MHC-I) molecules play a central role in the immune response to viruses and cancers. They present peptides on the surface of affected cells, for recognition by cytotoxic T cells. Determining which peptides are presented, and in what proportion, has profound implications for developing effective, medical treatments. However, our ability to predict peptide presentation levels is currently limited. Existing prediction algorithms focus primarily on the binding affinity of peptides to MHC-I, and do not predict the relative abundance of individual peptides on the surface of antigen-presenting cells in situ which is a critical parameter for determining the strength and specificity of the ensuing immune response. Here, we develop and experimentally verify a mechanistic model for predicting cell-surface presentation of competing peptides. Our approach explicitly models key steps in the processing of intracellular peptides, incorporating both peptide binding affinity and intracellular peptide abundance. We use the resulting model to predict how the peptide repertoire is modified by interferon-γ, an immune modulator well known to enhance expression of antigen processing and presentation proteins.