Abstract Influenza A virus particles assemble at the plasma membrane of infected cells. During assembly all components of the virus come together in a coordinated manner to deform the membrane into a protrusion eventually forming a new, membrane-enveloped virus. Here we integrate recent molecular insights of this process, particularly concerning the structure of the matrix protein 1 (M1), within a theoretical framework describing the mechanics of virus assembly. Our model describes M1 polymerization and membrane protrusion formation, explaining why it is efficient for M1 to form long strands assembling into helices in filamentous virions. Eventually, we find how the architecture of M1 helices is controlled by physical properties of viral proteins and the host cell membrane. Finally, by considering the growth force and speed of viral filaments, we propose that the helical geometry of M1 strands might have evolved to optimize for fast and efficient virus assembly and growth. Significance Influenza A virus remains a major threat to public health. Its most abundant viral protein, matrix protein 1 (M1), forms an endoskeleton underneath the viral membrane, but how this endoskeleton contributes to the virus’ lifecycle is poorly understood. Combining cryo-electron tomography data and structural data with theoretical predictions, we explain how the energetically favorable polymerization of M1 into helical strands mediates the membrane deformations that permit the virus to exit infected cells. Our analysis of M1’s variable architecture provides insights into adaptive strategies of the virus for efficient growth under variable local conditions. The quantitative framework developed in this study could be extrapolated to other enveloped viruses and generally applied to protein-driven membrane deformations.