An encountered-type haptic interface generates touch sensation only when a user's hand “encounters” virtual objects. This paper presents an effective encountered-type haptic interface that enables rendering of surfaces with variable curvature. The key idea is to systematically bend a thin elastic plate so as to create a curved surface with desired curvature, which becomes a contacting end effector that follows the user's finger and becomes an interface a user can touch when needed. The pose of the curvature is controlled in a way that it corresponds to the curved surfaces of virtual objects and user's finger position. The idea is realized by attaching two commercial haptic interfaces to both edges of a thin acryl plate and squeezing the plate. This setup allows us to generate a cylindrical object with curvature up to 0.035 mm-1 and gives 3DOF position control and 1DOF rotational control of the curved surface. Achievable workspace and curvature range are analyzed, and the feasibility and physical performance are demonstrated through a visuo-haptic grabbing scenario. In addition, a psychophysical experiment shows perceptual competence of the proposed system.