A black-body radiation (BBR) shifts of nsnp 3 P0 − ns 2 1 S0 clock transition in divalent atoms Mg, Ca, Sr, and Yb are evaluated. A theory of multipolar BBR shifts is developed and its implications are discussed. At room temperatures, the resulting uncertainties in the BBR shifts are relatively large and substantially affect the projected 10 −18 fractional accuracy of the optical-lattice-based clocks.PACS numbers: 06.30. Ft, 32.10.Dk, Atomic clocks based on ultranarrow [6,7]. In addition, various schemes of probing the highlyforbidden nsnp 3 P 0 − ns 2 1 S 0 clock transition have been proposed: three-photon transition, electromagneticallyinduced transparency, and transition assisted by external magnetic field [6,7,8].Considering advantages of optical lattice clocks, here we investigate an important systematic effect of the black-body radiation (BBR) on the frequency of the 3 P 0 − 1 S 0 clock transition. Indeed, the SI definition of the second explicitly involves atomic clock operating at the absolute zero of temperature. In a laboratory environment with an ambient temperature T , one needs to introduce the T -dependent BBR correction to the observed frequency. Here, using techniques of many-body relativistic atomic structure, we compute the BBR shift for Mg, Ca, Sr, and Yb and evaluate uncertainties of the calculations. As summarized in Table I, the resulting fractional uncertainties in the clock frequencies at T = 300 K are large, ranging from 1 × 10 −17 for Mg to 3 × 10 −16 for Yb.The main conclusions of this paper are (i) the present uncertainty in our computed BBR shift is an obstacle on the way towards the projected 10 −18 accuracy goal; (ii) due to T 4 scaling of the BBR shift, it may be beneficial to operate at low temperatures, e.g., at liquid nitrogen temperatures; (iii) if operating at room temperatures, high-precision (0.02%-accurate for Sr) measurements of the BBR shifts or related quantities are required; (iv) Mg-based clock is the least susceptible to BBR; compared to Sr, the Mg BBR shift is an order of magnitude smaller (see Table I). Additionally, we develop a general relativistic theory of the BBR shift caused by multipolar (EJ and MJ) components of the radiation field. δνBBR is the BBR shift at T = 300 K with our estimated uncertainties. ν0 is the clock transition frequency, and δνBBR/ν0 is the fractional contribution of the BBR shift. The last column lists fractional errors in the absolute transition frequencies induced by the uncertainties in the BBR shift.