We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multilamellar membrane structures. Under conditions of osmotic stress (swelling or dehydration), we find a stable, deformed state in which the layer deformation is given by deltaR infinity r(square root[B(A)/(hB)]), where B(A) is the area compression modulus, B is the interlayer compression modulus, and h is the repeat distance of layers. Also, above a finite threshold of dehydration (or osmotic stress), we find that the system becomes unstable to undulations, first with a characteristic wavelength of order square root[xi(d)0], where xi is the standard smectic penetration depth and d0 is the thickness of dehydrated region.