The NEA Working Party on Nuclear Criticality Safety (WPNCS) established an Expert Group on Source Convergence in Criticality Safety Analysis (EGSCCSA) to explore the problems of slow convergence and statistical fluctuations that can combine to produce unreliable source distributions and fission rates as well as underestimates of keff and its uncertainty. Aimed at fostering improved robustness of criticality safety analyses with respect to source convergence, the group's first task was to assemble four test problems that represent cases previously encountered in criticality safety analyses. They are intended to be used as a basis for comparison of source convergence performance rather than a comparison of physics results. The problems include a reactor fuel storage array, a spent fuel pin array, an aqueous processing system and an array of small fissile components. The results of the four test problems are described herein.