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This paper describes a four-axis flexible force sensor using conductive material. The contact part of this sensor is composed of silicon rubber. The measurement part of this sensor is composed of three layers including the conductive material which is made of mixture of polycarbonate and vapor grown carbon fiber (PC/VGCF). The PC/VGCF is used as a pressure-sensitive material. In addition, neural network is used to estimate four-axis contact forces in consideration of a complex deformation of the flexible contact part. In this paper, the structure and fundamental characteristics of each part of the sensor is described. The experiment of estimation of four-axis contact forces by using neural network is carried out. It is confirmed that this sensor and contact force estimation system using neural network has a possibility to identify four-axis contact force.