As the field of robotics continues to strive forward, the need for artificial tactile sensing becomes increasingly evident. Real-time, local processing of tactile sensory data also becomes a crucial issue in most applications of tactile sensing. In this thesis it is shown that analog neural networks provide an elegant solution to some of the problems of low level tactile data processing. We consider the particular problem of 'deblurring' strain data from an array of tactile sensors. It is shown that the inverse problem of deblurring strain measurements to recover the surface stress over a region of contact is ill-posed in the sense defined by Hadamard. This problem is further complicated by the corruption of sensor data by noise. We show that the techniques of 'regularization' may be used to introduce prior knowledge of the solution space into the solutions in order to transform the problem to one which is well-posed and less sensitive to noise. The particular regularizer chosen for the recovery of normal stress distributions is of the functional form of Shannon entropy. Formulation of the inverse problem so as to regularize the solutions result in a variational principles which must be solved in order to recover the surface stress. An analog neural network which provides the desired solutions to the variational principle as a course of natural time evolution of the circuit dynamics is proposed as a solution to the requirements for fast, local processing in tactile sensing. We discuss performance of the network in the presence of noise based upon computer simulations. We also demonstrate, by means of a breadboard prototype of the network, the speed of computation achievable by such a network. An integrated circuit implementation of the proposed network has been completed and the requirements of such implementations is discussed.