The bit-error- rate (BER) performance of 3-dimensional (3D) product codes under iterative bounded-distance decoding of the component codes is considered and a framework for analyzing the BER-performance is presented. The performance analysis of iterative decoding is based on a graphical model of the underlying 3D product code, which is a tripartite 3-uniform hypergraph. The BER performance for 3D product codes shows a threshold behavior. The thresholds can be approximated by an exit-chart-like technique from the parameters of the component codes. In the case of a symmetric product code, for which all three component codes are based on the same linear t-error correcting code, asymptotically for large code lengths, the BER-threshold is determined by the threshold for the appearance of a k-core with k=t + 1 in the graphical model.