  This work analyzes the asymptotic behaviors of the asymptotically flat
solutions of Einstein-\ae ther theory in the linear case. The vacuum solutions
for the tensor, vector, and scalar modes are first obtained, written as sums of
various multipolar moments. The suitable coordinate transformations are then
determined, and the so-called pseudo-Newman-Unti coordinate systems are
constructed for all radiative modes. In these coordinates, it is easy to
identify the asymptotic symmetries. It turns out that all three kinds of modes
possess the familiar Bondi-Metzner-Sachs symmetries or the extensions as in
general relativity. Moreover, there also exist the \emph{subleading} asymptotic
symmetries parameterized by a time-independent vector field on a unit 2-sphere.
The memory effects are also identified. The tensor gravitational wave also
excites similar displacement, spin, and center-of-mass memories to those in
general relativity. New memory effects due to the vector and scalar modes
exist. The subleading asymptotic symmetry is related to the (leading) vector
displacement memory effect, which can be viewed as a linear combination of the
electric-type and magnetic-type memory effects. However, the scalar memory
effect seems to have nothing to do with the asymptotic symmetries at least in
the linearized theory.
