The latent potential for every military actor, as well as for the resources controlled by military organizations, to be sacrificed by the state for political or existential purposes constitutes the central collective signifier of military existence. This potential is not merely vague fears and premonitions of a possible future but also a real mode of operation, most often distant, sometimes imminent, and on rare occasions, a reality. This looming possibility does not, however, imply simple or immediate consequences. It makes up an ever-present collective imagination – both shared and contested – and infused with collective emotions such as fear, pride, and a sense of duty. More formally, it could be described as a central imaginary signification, articulated in countless ways that ascribe meaning to the military as a social practice. The institutional specificity of the military is a deeply ingrained transformative capacity, not hierarchy, uniforms, or lethal weapons. There is nothing, literally, that is military per se. Military institutional specificity is thus a state of becoming – a potential in which anything within military organizations can be enrolled as part of a war machine. The perceived proximity to this war machine is ‘the shadow of war’: a simultaneously elusive and overwhelming source of meaning within all military organizations. The paper explores the becoming of military institutional specificity through the concepts of institutional transversality, affinity, and specificity.