Birds migrating over land use either of two basic flight strategies, i.e. flapping or gliding/soaring flight. In soaring flight the birds gain altitude mainly by circling in thermals, i.e. rising air, and then they glide off until another thermal is encountered. Powered flapping flight is energetically much more expensive than gliding flight. This leaves us with the question why do not most birds adopt the soaring strategy rather than flapping flight on migration? I present optimization criteria, based on flight mechanical theory, for (i) energy-selected migration and (ii) time-selected migration, for flapping and soaring flight migration, respectively. These are evaluated in relation to general body size and rate of climb in thermals. I also consider the effects of wing morphology and horizontal winds. The general conclusion is that minimization of transport costs probably cannot be the only critical selective factor. In time-selected migration the size range of birds for which flapping flight is advantageous over thermal soaring flight, is significantly larger than in energy-selected migration, and this is in better agreement with what is found in real birds. Therefore, resulting migration speed probably constitutes an important selective force in bird migration. I also evaluate criteria for mixed strategies, i.e. when birds should use soaring flight when thermals are available and proceed by flapping flight otherwise. Finally, I also discuss some other factors, e.g. sensitivity to crosswinds, abundance of thermals and topography, which may affect the evolution of migration strategy.