The shape dynamics of fluid vesicles is governed by the coupling of th
e how within the two-dimensional membrane to the hydrodynamics of the
surrounding bulk fluid. We present a numerical scheme which is capable
of solving this flow problem for arbitrarily shaped vesicles using th
e Oseen tensor formalism. For the particular problem of simple shear f
low, stationary shapes are found for a large range of parameters. The
dependence of the orientation of the vesicle and the membrane velocity
on shear rate and vesicle volume can be understood from a simplified
model.