The objective of this work is to examine the potential of isogeometric methods in the context of multidisciplinary shape optimization. We introduce a shape optimization problem based on a coupled fluid-structure system, whose geometry is defined by NURBS (Non-Uniform Rational B-Spline) curves. This shape optimization problem is then solved by using either an isogeometric approach, or a classical grid-based approach. In spite of the fact that optimization results do not show any major differences, conceptional advantages of the new isogeometric method become apparent. In particular, control points of the spline can be directly handled as design variables without the need of a spline-fit and consequently geometry errors can be excluded at every stages of the optimization loop.