A neutron activation analysis (NAA) of three samples of human remains of the 16th and 17th centuries from the necropolises of the Moscow Kremlin has been carried out at FLNP JINR. The samples were irradiated at two facilities: the IREN source of resonance neutrons and the IBR-2 reactor. Spectra of the induced activity of the irradiated samples were measured by using the automatic measurement system developed at the Frank Laboratory of Neutron Physics (FLNP) of the Joint Institute for Nuclear Research (JINR). This system consists of a high-purity germanium detector with spectrometric electronics, a sample changer, and control software. Mass fraction of arsenic, mercury, and some other elements were calculated using two NAA methods—relative and absolute. The obtained values confirm the fact of acute mercury poisoning of Anastasia Romanovna, the first wife of Tsar Ivan Vasil’evich the Terrible, the first Russian Tsarina (died in 1560). High levels of mercury were detected in the bone remains of Tsarevich Ivan Ivanovich (died in 1581), the son of Tsar Ivan the Terrible, and Prince Mikhail Vasil’evich Skopin-Shuiskii (died in 1610). The results provide an opportunity to introduce into scientific circulation the exact values of mass fraction of mercury, arsenic, and other elements in the samples taken from the burials of the Russian historical figures of the second half of 16th–early 17th century.