  Numerical study of the hydrodynamics of thin sheets and ribbons presents
difficulties associated with resolving multiple length scales. To circumvent
these difficulties, asymptotic methods have been developed to describe the
dynamics of slender fibres and ribbons. However, such theories entail
restrictions on the shapes that can be studied, and often break down in regions
where standard boundary element methods are still impractical. In this paper we
develop a regularised stokeslet method for ribbons and sheets in order to
bridge the gap between asymptotic and boundary element methods. The method is
validated against the analytical solution for plate ellipsoids, as well as the
dynamics of ribbon helices and an experimental microswimmer. We then
demonstrate the versatility of this method by calculating the flow around a
double helix, and the swimming dynamics of a microscale "magic carpet".
