The moments of inertia of the Moon can be computed using various subsets of the degree two harmonics of the gravity field and the librational parameters. Recent estimates of these parameters allow four different solutions for the three principal moments of inertia. The solutions disagree by about 15 times the formal errors in the solutions. A possible resolution of these discrepancies involves nonrigid librational motion, either in the form of an elastic toroidal strain or with a fluid core which is only partially coupled to the rigid mantle. For this explanation to be viable, it must involve preferential strain in association with the longitudinal librations. Both gravitational and viscous coupling between a fluid core and a solid mantle are expected to have that behavior.