Geographers have increasingly attended to the role of emotion in geopolitical encounters and the geopolitics of cross‐border infrastructure projects. While scholars have theorised fear as an emotion produced by elite geopolitical discourses and encounters between bodies, we know much less about how infrastructure's materialities provoke fear and anxiety. Furthermore, key distinctions between anxiety – or a psychological state of insecurity and unease – and fear, which is attached to a specific target object, are still not fully understood. Focused on the uncertainties over China's Belt and Road Initiative (BRI), we develop the concept of sovereign anxiety – a generalised condition of unease over the security of one's political community – to account for how the BRI generates not only the hard materials of infrastructure (e.g., roads, dams and pipelines), but also the social practices of affect and emotion. Sovereign anxiety, we argue, is heightened by the absence of transparency over China's infrastructure investments in Myanmar. In this paper, we trace how sovereign anxiety is variously experienced and grounded in residents' observations, personal biographies, social histories, and sense of community belonging. We also identify three themes by which fears of the BRI are articulated: relations, roads, and resources. This article contributes an emotional geopolitics perspective to grounded studies of the BRI, while also demonstrating the geopolitical significance of attending to the emotional lives of infrastructure in relation to the BRI and beyond.