Calculations of potential ow and pressure over multi-element airfoils are studied, using conformal maps. A composition of classical Karman-Tre tz maps is used to smooth out the trailing edge corners successively, from each of the m airfoils, producing a multiply connected domain with nearly circular boundaries. A Fourier/Laurent series method is then used to map a domain exterior to nonoverlapping disks to the exterior of the domain with smooth boundaries. The computations of potential ow and pressure are done in the domain with circular boundaries and then carried over to the physical space, using the conformal maps. In practice, this technique can be used as a rst approximation to the solution in more complicated airfoil con gurations.