Intracellular events that take place during influenza virus replication in mammalian cells are well understood qualitatively. However, to better understand the complex interaction of the virus with its host cell and to quantitatively analyze the use of cellular resources for virion formation or the overall dynamics of the entire infection cycle, a mathematical model for influenza virus replication has to be formulated. Developed in the present study is the first structured model for the single cell reproductive cycle of influenza A virus in mammalian cells that accounts for all the individual steps of the process, such as attachment, internalization, genome replication and translation, and progeny virion assembly. The model describes an average cell surrounded by a small quantity of medium and infected by a low number of virus particles. It makes possible to determine the basic laws that control the dynamics of virus replication. The model allows estimating the number of cellular resources consumed by virus replication and to reveal factors that limit the growth rate of progeny virus particles and virus release. Based on the model it is also possible to analyze effects of parameter changes on the dynamics of virus replication, and, using this knowledge, to formulate hypotheses concerning the optimization of vaccine production processes. The single cell model and the results of simulations based on it provide the prerequisite for several useful model modifications. One of such modifications is a population model, taking into account the populations of uninfected, infected, and dead cells, as well as the population of free virus particles. The population model, particularly, provides a possibility to investigate the dynamics of virus production by a cellular system at different number of seeded virions per cell. Furthermore, having revealed the most critical steps of virus replication, it is possible to formulate a reduced single cell model, which adequately reproduces the dynamics of the process. Possessing a simple structure, the reduced model can be used for the development of structured population balance models describing the interaction of infected cells. The single cell model for the influenza virus life cycle and its modifications facilitate future studies of influenza virus replication at a cellular level. A more detailed insight into the interactions of viruses and host cells might help to improve the understanding of virus-related diseases, to develop therapies against them, and to identify possible targets for molecular engineering. Model equations can be easily modified to include new experimental results, as well as to examine different hypotheses concerning cellular or viral replication mechanisms. Finally, the model can be used as a starting point for modeling infection cycles of other viruses.