In this paper, the mutual-impedances within arrays of sonar transducers are calculated by integration on neural networks. The multi-dimensional integrations appearing in mutual-impedance formulations are replaced by integration on neural networks. Initially, the integrand is modeled by a trained neural network. The multi-dimensional integrations on the integrand can then be replaced by integrations on the output of neural network. Neither numerical nor artificial integration operation is required. With this replacement, the computation efforts are well reduced. Numerical examples show that the results calculated by the proposed method in this paper are consistent with those calculated by other existing studies. The method proposed in this paper can be easily applied to many other engineering problems.