  We investigate the existence of higher order topological localized modes in
moir\'{e} lattices of bilayer elastic plates. Each plate has a hexagonal array
of discrete resonators and one of the plates is rotated an angle
($21.78^\circ$) which results in a periodic moir\'{e} lattice with the smallest
area. The two plates are then coupled by inter-layer springs at discrete
locations where the top and bottom plate resonators coincide. Dispersion
analysis using the plane wave expansion method reveals that a bandgap opens on
adding the inter-layer springs. The corresponding topological index, namely
fractional corner mode, for bands below the bandgap predicts the presence of
corner localized modes in a finite structure. Numerical simulations of
frequency response show localization at all corners, consistent with the
theoretical predictions. The considered continuous elastic bilayered moir\'{e}
structures opens opportunities for novel wave phenomena, with potential
applications in tunable energy localization and vibration isolation.
