A flexible heat pipe is disclosed for use with evaporator and condenser elements for removing heat from electronic components. The flexible heat pipe comprises a bellows member fixed at one end to a condenser member and at an opposite end to an evaporator member. A cable artery is disposed within the bellows and is fixed at one end to the evaporator, and slidingly engages the condenser at the opposite end. The bellows acts as a flexible vapor envelope, and the cable artery acts as a flexible wick for directing condensed working fluid from the condenser back to the evaporator. The sliding connection between the cable artery and the condenser allows relative axial movement, and the inherent flexibility of the cable artery allows relative lateral movement. Thus, the condenser and evaporator can move in all directions with respect to each other, which can provide desired vibration isolation of the two components.