In order to improve the intelligence of a robot with a sense of touch, we have developed a tactile sensor array which can detect the distribution of the three components of a force vector. The tactile sensor consists of a 6×15 matrix of 3×3 mm sensing sites; each site is made of two single-crystal silicon rings on which semiconductor strain gauges are formed by means of a semiconductor processing technique. In this paper, we have introduced formulas to calculate applied force/moment, a center of distributed pressure, and some parameters of slip and hardness, and then carried out sensing tests in order to validate those formulas. Experimental results show that applied force/moment and the center of distributed pressure can be detected with practical accuracy. Slipping, rolling and rotating states can be distinguished by combinations of the slip parameters. Moreover, mechanical properties can be sensed by means of combinations of the hardness parameters. A lump in a soft object can be recognized using an adequate threshold method.