  In this paper, we study biharmonic maps into Sol and Nil spaces, two model
spaces of Thurston's 3-dimensional geometries. We characterize non-geodesic
biharmonic curves in Sol space and prove that there exists no non-geodesic
biharmonic helix in Sol space. We also show that a linear map from a Euclidean
space into Sol or Nil space is biharmonic if and only if it is a harmonic map,
and give a complete classification of such maps.
