Currently knowledge management and discovery plays crucial role in different industries. Apart from that in many cases decisions made by companies in mission critical areas (like nuclear power industry, medicine and finance, to name a few) should be verified by domain expert and/or explained. This is needed to fulfill regulatory requirements, to verify correctness and / or discover new knowledge. Artificial neural networks are well known models that can be used to solve classification problems. Unfortunately they are “black box” models for end users, because classification process is fully hidden from the observer and cannot be easily mapped into formalized meaningful form that can be understood by the domain expert. There are multiple knowledge representations, and the one chosen to work with in this study is elliptical rules. A set of such rules can be used to determine the class of an input data point by the determination of ellipsoid that covers provided point. Current paper addresses the problem of elliptical rules (ER) extraction from trained artificial radial basis function neural network (RBFNN). This study uses RBFNN with tunable nodes - such networks are built using orthogonal forward feature selection algorithm and they usually have much less neurons (in comparison to RBFNNs containing neurons with fixed radii) while having comparable or even superior accuracy. The article poses non-convex optimization problem of finding multiple ellipsoids of largest volume inscribed into RBFNN decision boundary. Non-convexity arises due to complex nature of RBFNN decision boundary which serves as constraint. Further we describe an algorithm for extraction of ER from trained RBFNN. The provided experimental results show that few of the extracted elliptical rules have comparable and in some cases higher classification accuracy than original RBFNN. Although curse of dimensionality is applicable to the provided algorithm, experiments have shown that it can be readily used for relatively low-dimensional problems. Finally are described the possible future research directions.