Maintaining integrity of the plasma membrane is essential for cell life. Thus, efficient cell membrane repair mechanisms are crucial for handling membrane disruptions resulting from external perturbations of eukaryotic cells. Cancer cells in particular, experience enhanced membrane stress when navigating through the dense extracellular matrix, which increases the frequency of membrane injuries. Yet the underlying molecular details of plasma membrane repair are not well understood. Plasma membrane injury followed by Ca2+ influx, activates the recruitment of Annexins to membrane wound edges. In cells, we find that Annexin A4 binding promotes repair of lesions generated by local laser treatment or other types of controlled damage. In planar model membranes, we show that curvature stress induced by annexin-binding leads to roll-up of the membrane as initiated from free membrane edges. The observation of rolling identify plasma membrane curvature near hole-edges as a potential key event in the plasma membrane repair (PMR) process. In the geometry of a membrane hole we propose that curvature leads to the formation of a characteristic neck structure around the hole as the first step in the repair process. Here we examine the phenomenon of annexin-induced membrane curvature near edges. This includes results obtained from model membranes, cells studies and theoretical modeling of curvature near a hole. Together, the results provide an enhanced mechanistic insight into the role of annexins for initiating membrane repair.