At present spent nuclear cores from Alfa class submarines are being stored in temporary facilities, designed to sore them only for a few years (3 to 5 years). This paper assesses the problems of nuclear safety during long-term unplanned forced storage of spent fuel because of the delay in building permanent facilities. The Nuclear Submarines (NS) cores use heavy liquid metal lead-bismuth coolant in the primary circuit of nuclear reactor. The radiation parameters of the discharged cores from NS of the Project 705K (this is the number of ship engineering design) are determined. Based on that determination a step-by-step solution is proposed and the technological and other challenges that the Project faces are considered.