  We develop a low-energy continuum model for phonons in twisted moir\'e
bilayers, based on a configuration-space approach. In this approach,
interatomic force constants are obtained from density functional theory (DFT)
calculations of untwisted bilayers with various in-plane shifts. This allows
for efficient computation of phonon properties for any small twist angle, while
maintaining DFT-level accuracy. Based on this framework, we show how the
low-energy phonon modes, including interlayer shearing and layer-breathing
modes, vary with the twist angle. As the twist angle decreases, the frequencies
of the low-energy modes are reordered and the atomic displacement fields
corresponding to phonon eigenmodes break translational symmetry, developing
periodicity on the moir\'e length scale. We demonstrate the capabilities of our
model by calculating the phonon properties of three specific structures:
bilayer graphene, bilayer molybdenum disulfide (MoS$_2$), and molybdenum
diselenide-tungsten diselenide (MoSe$_2$-WSe$_2$).
