Intracellular events that take place during influenza virus replication in animal 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 dynamic for the entire infection cycle, a mathematical model for influenza virus replication has to be formulated. Here, we present a structured model for the single-cell reproductive cycle of influenza A virus in animal cells that accounts for 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. The model allows estimation of the cellular resources consumed by virus replication. Simulation results show that the number of cellular surface receptors and endosomes, as well as other resources, such as the number of free nucleotides or amino acids, is not significantly influenced by influenza virus propagation. A factor that limits the growth rate of progeny viruses and their release is the total amount of matrix proteins (M1) in the nucleus while other newly synthesized viral proteins (e.g., nucleoprotein NP) and viral RNAs accumulate. During budding, synthesis of vRNPs (viral ribonucleoprotein complexes) represents another limiting factor. Based on this model it is also possible to analyze effects of parameter changes on the dynamics of virus replication, to identify possible targets for molecular engineering, or to develop strategies for improving yields in vaccine production processes. Furthermore, a better insight into the interactions of viruses and host cells might help to improve our understanding of virus-related diseases and to develop therapies.