We analyse a generic motility model, with the motility mechanism arising by contractile stress due to the interaction of myosin and actin. A hydrodynamic active polar gel theory is used to model the cytoplasm of a cell and is combined with a Helfrich-type model to account for membrane properties. The overall model allows to consider motility without the necessity for local adhesion. Besides a detailed numerical approach together with convergence studies for the highly nonlinear free boundary problem, we also compare the induced flow field of the motile cell with that of classical squirmer models and several microorganisms and identify the motile cell as a puller or pusher, depending on the strength of the myosin-actin interactions