Two dimensional magnetohydrodynamic simulations are presented of the distortion of a magnetic flux rope that is being accelerated through ambient solar wind plasma. The flux rope magnetic field has an axial component parallel to the solar wind field and an azimuthal component, which lies in the simulation plane. As the flux rope moves through the solar wind plasma, vortices form on its trailing edge and couple strongly to its interior. If the flux rope azimuthal field is weak, it deforms into an elongated banana-like shape after a few Alfv¿n transit times. A strong azimuthal field component tends to inhibit this distortion. If the flux rope is taken to model a magnetic cloud, it is suggested that the shape of the cloud at 1 AU is determined by its distortion in the inner solar wind. Distortion timescales beyond 1 AU are estimated as many days. It is estimated that effective drag coefficients somewhat greater than unity are appropriate for modeling flux rope propagation. ¿ American Geophysical Union 1995