The Plateau–Rayleigh instability was first proposed in the mid-1800s to describe how a column of water breaks apart into droplets to lower its surface tension. This instability was later generalized to account for the constant volume rearrangement of various one-dimensional liquid and solid materials. Here, we report a growth phenomenon that is unique to one-dimensional materials and exploits the underlying physics of the Plateau–Rayleigh instability. We term the phenomenon Plateau–Rayleigh crystal growth and demonstrate that it can be used to grow periodic shells on one-dimensional substrates. Specifically, we show that for certain conditions, depositing Si onto uniform-diameter Si cores, Ge onto Ge cores and Ge onto Si cores can generate diameter-modulated core–shell nanowires. Rational control of deposition conditions enables tuning of distinct morphological features, including diameter-modulation periodicity and amplitude and cross-sectional anisotropy. Our results suggest that surface energy reductions drive the formation of periodic shells, and that variation in kinetic terms and crystal facet energetics provide the means for tunability.