Haptic stimuli with directional content, e.g. navigational cues, may be difficult to use in handheld applications; the user's hand, where the cues are delivered, may not be aligned with the world, where the cues are to be interpreted. In such a case, the user would be required to mentally transform the stimuli between different reference frames. We examine the mental rotation of directional haptic stimuli in three experiments, investigating: 1. users' intuitive interpretation of rotated stimuli, 2. mental rotation of haptic stimuli about a single axis, and 3. rotation about multiple axes. We conclude that directional haptic stimuli are suitable for use in mobile applications, although users do not naturally interpret rotated stimuli in any one universal way. We find evidence of cognitive processes involving the rotation of analog, spatial representations. For small angles, these mental rotations come at little cost, but rotations with larger misalignment angles impact user performance. When considering the design of a handheld haptic device, hand pose must be carefully considered, as certain poses increase the difficulty of stimulus interpretation. All tested joint rotations impact task difficulty, but finger flexion and wrist rotation interact to greatly increase the cost of stimulus interpretation; such hand poses should be avoided when designing a haptic interface.