Influenza is a lipid-enveloped, pleomorphic virus. We combine electron cryotomography and analysis of images of frozen-hydrated virions to determine the structural organization of filamentous influenza A virus. Influenza A/Udorn/72 virions are capsule-shaped or filamentous particles of highly uniform diameter. We show that the matrix layer adjacent to the membrane is an ordered helix of the M1 protein and its close interaction with the surrounding envelope determines virion morphology. The ribonucleoprotein particles (RNPs) that package the genome segments form a tapered assembly at one end of the virus interior. The neuraminidase, which is present in smaller numbers than the hemagglutinin, clusters in patches and are typically present at the end of the virion opposite to RNP attachment. Incubation of virus at low pH causes a loss of filamentous morphology, during which we observe a structural transition of the matrix layer from its helical, membrane-associated form to a multilayered coil structure inside the virus particle. The polar organization of the virus provides a model for assembly of the virion during budding at the host membrane. Images and tomograms of A/Aichi/68 X-31 virions show the generality of these conclusions to non-filamentous virions.