The high efficiency of monocoque cylindrical shells in carrying axial loads is curtailed by their extreme sensitivity to imperfections. For practical applications, this issue has been alleviated by introducing closely stiffened shells which, however, require expensive manufacturing. Here we present an alternative approach that provides a fundamentally different solution. We design symmetry-breaking wavy cylindrical shells that avoid imperfection sensitivity. Their cross-section is formulated by NURBS interpolation on control points whose positions are optimized by evolutionary algorithms. We have applied our approach to both isotropic and orthotropic shells and have also constructed optimized composite wavy shells and measured their imperfections and experimental buckling loads. Through these experiments we have confirmed that optimally designed wavy shells are imperfection-insensitive. We have studied the mass efficiency of these new shells and found them to be more efficient than even a perfect circular cylindrical shell and most stiffened cylindrical shells.