Artificial sheet materials, known as MetaSurfaces, have been applied to fully control both space and surface waves due to their exceptional abilities to dynamically tailor wave fronts and polarization states, while maintaining small footprints. However, previous and current designs and manufactured MetaSurfaces are limited to specific types of surfaces. There exists no general but rigorous design methodology for MetaSurfaces with generic curvature. The aim of this paper is to develop an analytical approach to characterize the wave behavior over arbitrary curvilinear MetaSurfaces. The proposed method allows us to fully characterize all propagating and evanescent wave modes from the MetaSurfaces. We will validate the proposed technique by designing, realizing and testing an ultrathin MetaSurface cloak for surface waves. Good results are obtained in terms of bandwidth, polarization independence and fabrication simplicity.