A neural network of a model point reactor with instantaneous feedback on power was built in order to investigate and illustrate the possibilities of neutral networks in application to problems of reactor physics. A neural network is tested for its ability to predict a reactor’s capacity in the presence of uncontrolled perturbations of the reactor’s reactivity and errors of power measurements as well as for its use outside its training range. The obtained results show that in terms of accuracy a neural network model under the same conditions is highly competitive with or can appreciably surpass simple analytical assessments.