  An analytical approach is presented to model a metasolid accounting for
anisotropic effects and rotational mode. The metasolid is made of either
cylindrical or spherical hard inclusions embedded in a stiff matrix via soft
claddings, and the analytical approach to study the composite material is a
generalization of the method introduced by Liu \textit{et al.} [Phys. Rev. B,
71, 014103 (2005)]. It is shown that such a metasolid exhibits negative mass
densities near the translational-mode resonances, and negative density of
moment of inertia near the rotational resonances. The results obtained by this
analytical and continuum approach are compared with those from discrete
mass-spring model, and the validity of the later is discussed. Based on derived
analytical expressions, we study how different resonance frequencies associated
with different modes vary and are placed with respect to each other, in
function of the mechanical properties of the coating layer. We demonstrate that
the resonances associated with additional modes taken into account, that is,
axial translation for cylinders, and rotations for both cylindrical and
spherical systems, can occur at lower frequencies compared to the previously
studied plane-translational modes.
