In this paper, we implement an ungrounded pen-shaped kinesthetic display and construct a three-dimensional (3D) haptic interaction system. The ungrounded pen-shaped kinesthetic display provides kinesthetic sensations to a user's fingers without the use of mechanical linkages. Therefore, the user can move his/her hand freely in air and interact with virtual environments with sensation of touching. We verified the ability of the device to provide forces and to represent a virtual surface for 3D input. Then we constructed a 3D haptic interaction system in that the user can touch virtual objects displayed as 3D images directly. We also applied the device to an interface for 3D modeling and constructed a 3D haptic modeling system in that the user can create touchable 3D models by sketching two-dimensional (2D) figures in air.