The high degree of conservation of CD8 T cell epitopes of influenza A virus (IAV) may allow for the development of T cell-inducing vaccines that provide protection across different strains and subtypes. This conservation is not fully explained by functional constraint, since an additional mutation(s) can compensate for the replicative fitness loss of IAV escape variants. Here, we propose three additional mechanisms that contribute to the conservation of CD8 T cell epitopes of IAV. First, influenza-specific CD8 T cells may protect predominantly against severe pathology rather than infection and may have only a modest effect on transmission. Second, polymorphism of the human major histocompatibility complex class I (MHC-I) gene restricts the advantage of an escape variant to only a small fraction of the human population who carry the relevant MHC-I alleles. Finally, infection with CD8 T cell escape variants may result in a compensatory increase in the responses to other epitopes of IAV. We use a combination of population genetics and epidemiological models to examine how the interplay between these mechanisms affects the rate of invasion of IAV escape variants. We conclude that for a wide range of biologically reasonable parameters, the invasion of an escape variant virus will be slow, with a timescale of a decade or more. The results suggest T cell-inducing vaccines do not engender the rapid evolution of IAV. Finally, we identify key parameters whose measurement will allow for more accurate quantification of the long-term effectiveness and impact of universal T cell-inducing influenza vaccines.IMPORTANCE Universal influenza vaccines against the conserved epitopes of influenza A virus have been proposed to minimize the burden of seasonal outbreaks and prepare for the pandemics. However, it is not clear how rapidly T cell-inducing vaccines will select for viruses that escape these T cell responses. Our mathematical models explore the factors that contribute to the conservation of CD8 T cell epitopes and how rapidly the virus will evolve in response to T cell-inducing vaccines. We identify the key biological parameters to be measured and questions that need to be addressed in future studies.