Wrinkling of thin membranes due to different in- plane loadings and boundary conditions has drawn attention of researchers in structural engineering since the development of thin webs for early aircraft structures. More recently, pre-stressed lightweight membrane structures have been proposed for future space missions, for example solar sails, the next generation space telescope sunshield and space-based radar systems. These structures are often partially wrinkled during operation. The formation of wrinkles alters the load paths and the structural stiffness of the membranes. More importantly its occurrence degrades the surface accuracy of these structures, which is a key design parameter. This book focuses on wrinkling of thin silicone rubber membranes subjected to uniaxial tensile load with clamping boundary condition, and investigates the onset and profiles of wrinkles using both experimental and numerical approaches. An idea of suppressing wrinkle instabilities of dielectric elastomer membranes using through- thickness electric field was proposed and verified in both experiments and numerical simulations.