A new technique has been developed for the measurement of the thermal conductivity of lunar core samples. According to this technique, the core sample is heated radiatively from the outside at a known rate, the temperature is measured at the surface of the coretube, and the thermal conductivity of the sample is determined by comparing the measured temperature with the theory. The technique conforms with the aims of lunar sample preservation in that the sample remains intact after the measurements. The solution, as obtained in this paper, of a thermal conduction equation for a composite circular cylinder, with zero initial temperature and a constant heat-flux at its outer boundary, provides a theoretical basis for the present technique. Because of their mathematical similarity, the corresponding problems for a composite slab or sphere were also solved and the solutions are presented for possible future application to the thermal conductivity measurements. Testing demonstrated the feasibility of the new technique. The thermal conductivity of a simulant lunar soil sample, as determined by the present technique under vacuum conditions at about 300 K for sample densities of 1.47-1.67 g cm
-3
, is 2.05-2.65 x 10
-3
W m
-1
K
-1
, which compares favourably with that of the same sample, 1.61-2.89 x 10
-3
W m
-1
K
-1
at sample densities of 1.50-1.75 g cm
-3
, as measured under similar conditions by the standard line heat source technique. We describe in detail the experimental apparatus construction and procedure; in particular, the number of precautions taken to preserve the samples from disturbances and to improve the measurement results. This technique was successfully applied to the thermal conductivity measurement of two Apollo 17 drill-core samples. The results, 1.9-4.9 x 10
-3
W m
-1
K
-1
, which is intermediate between the values of thermal conductivity of the lunar regolith determined
in situ
(0.9-1.3 x 10
-2
W m
-1
K
-1
and those of lunar soil samples measured in the laboratory under simulated lunar surface conditions (0.8-2.5 x 10
-3
W m
-1
K
-1
) presents an important clue to the understanding of heat transportation mechanisms in the lunar regolith.
