A patient interface device for an ophthalmic surgical laser system includes a lens cone component for coupling to the laser system and a suction ring component for coupling to the patient’s eye. The suction ring includes a gripper with an opening for receiving and retaining the lens cone, and a flexible skirt joined to the gripper for coupling to the eye with a vacuum force. The flexible skirt includes a circular inner edge and a circular outer edge for contacting the eye surface, and a plurality of circumferentially distributed scleral support protrusions protruding from a circumferential side wall. The end surface of the scleral support protrusions are sloped in a side cross-sectional view. The scleral support protrusions have a length to width ratio from 1.1 to 2.1, and an arc-angle ratio of the scleral support protrusions to the gaps between them is from 2.2 to 3.0. The scleral support protrusions contact the surface of the eye when the skirt is docked to the eye, which minimize intraocular pressure increase due to docking and applanation while still achieving a good vacuum seal between the suction ring and the eye. The scleral support protrusions function to prevent major deformation of the sclera when the cornea is applanated.