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In the study of rotational motion of the Moon is not given sufficient attention on the impact of elastic properties of the mantle of the moon on the amplitudes and periods of forced and free librations. So the authors of the empirical theory of libration of the Moon, based on the long series of laser observations of the Moon (over 40 years) are limited by simple observation of the possible influence of the moon on the elastic properties of the libration of the Moon: "The elastic deformation and presenve of the core alter these periods by small amounts (Williams et al. 2001). "(Rambaux, Williams, 2011, p. 89). In this paper, we show that the corrections to the values of the period of free libration of the pole of the moon is quite significant and should be considered in high-precision theories of libration, by the processing of laser observations of the Moon and in studies of the Moon's rotation directly from the surface of the Moon (in Japanese project ILOM (Hanada et al ., 2006; Petrova, Hanada et al., 2011). The effects of the elasticity of the Moon in motion of its pole have been studied by two models: 1. Elastic Moon (no liquid core) and 2. Moon with an elastic mantle and liquid core. We concentrate here attention on long-periodic (Chandler) pole motion.