A flexible aerodynamic surface is considered as a possible means of delaying transition and reducing skin-friction drag. The results of an extensive analytical study on boundary-layer instability and transition in incompressible Blasius-flow over a flexible surface are presented. A simple flexible skin model consisting of a taut membrane and an elastic base has been considered. The mechanical behavior of such a skin is controlled by the mass, the wave propagation velocity, the stiffness, and the damping. The analysis shows that with proper selection of the surface characteristics, the transition can be significantly delayed through reduced amplification rates, even though the critical Reynolds number for instability is only slightly increased. The extent of transition delay and the required surface properties are delineated. The theoretically possible drag reduction is most significant within the Reynolds number range of 3 to 50 X 10 6. Hence, potential fields of application of flexible skins would be in sailplanes, helicopters, small and medium subsonic airplanes, hydrofoils, torpedoes, speed boats, and miniature submarines. Nomenclature a = amplification factor, imaginary part of the complex wave velocity cr = phase velocity, real part of the complex wave velocity Com = wave propagation velocity in the membrane, (T/M)l/<2 d = damping coefficient, Eq. (21) D = damping constant, lb-sec/ft3 KM = mass parameter, Eq. (13) Ks = stiffness parameter, Eq. (15) KD = damping parameter, Eq. (17) m = mass coefficient, Eq. (18) M = membrane mass per unit area, Ib-sec2/ft3 Rx = Reynolds number based on length, Um x/v Rd = Reynolds number based on boundary-layer thickness S = compression stiff ness of base material, Ib/ft3 T = membrane tension, Ib/ft t/oo = freestream velocity, fps x = distance from leading edge along the plate, ft a. = dimensionless wave number, kd /3r = disturbance frequency, a.cr d = boundary-layer thickness, ft d* = boundary-layer displacement thickness, ft v — kinematic viscosity of fluid, ft2/sec p = density of fluid, Ib-sec2/ft3 coo = dimensionless cutoff frequency, (S/M)ll2d/Uo3 w* = circular frequency of disturbance, sec1 ior = dimensionless circular frequency, (3r/Rd = co^v/U m2