In physical human-machine interaction applications, the accurate measurement of interactive forces between the human and the machine plays a significant role. Sensors for this purpose should not only be accurate and reliable, but also be soft enough to guarantee the safe and compliant interaction. In this aspect, pneumatic sensors with soft air chambers have often been utilized as a soft force sensor system. Although the pneumatic-based force sensor provides a good compliance and softness, however, it measures only a lumped force acting on the chamber, because the pneumatic sensor measures the overall pressure change in the air chamber. In this paper, a three-axis force sensor with three air chambers in a radially symmetric pattern is proposed for the measurement of multi-dimensional interaction forces with high softness and compliance. Each air chamber embeds a pneumatic sensor, and the pressure changes in the three air chambers are measured in order to distinguish the direction of the applied force. By decoupling the sensor signals from the three pneumatic sensors, the three-dimensional force components can be calculated accurately. Consequently, the proposed sensor is able to measure the three-dimensional forces while maintaining the great softness and compliance provided by the soft air chambers. The design, the fabrication method, and the verification of the proposed method are introduced in this paper.