  In present article we consider the problems of concentrated point force which
is moving with constant velocity and oscillating with cyclic frequency in
unbounded homogeneous anisotropic elastic two-dimensional medium. The
properties of plane waves and their phase, slowness and ray or group velocity
curves for 2D problem in moving coordinate system are described. By using the
Fourier integral transform techniques and established the properties of the
plane waves, the explicit representation of the elastodynamic Green's tensor is
obtained for all types of source motion as a sum of the integrals over the
finite interval. The dynamic components of the Green's tensor are extracted.
  The stationary phase method is applied to derive an asymptotic approximation
of the far wave field. The simple formulae for Poynting energy flux vectors for
moving and fixed observers are presented too. It is noted that in the far zones
the cylindrical waves are separated under kinematics and energy.
  It is shown that the motion bring some differences in the far field
properties. They are modification of the wave propagation zones and their
number, fast and slow waves appearance under trans- and superseismic motion and
so on.
