We formulate the resonances of three simple geometrical inclusions (a plane, a cylinder and a sphere) and find several clues to distinguishing the shape of volcanic fluid systems and their relevance to the observation of long-period earthquakes. The series of eigenfrequencies for a cylindrical and a spherical inclusion have shifts of π/4 and π/2, respectively, in their higher modes from the eigenfrequencies of a planar inclusion. The ratios between the higher and fundamental characteristic frequencies can be indicators of the geometry of volcanic fluid inclusions. Furthermore, the eigenattenuation factor of a planar inclusion is a constant value that is determined uniquely by the impedance contrast between the fluid and the surrounding elastic medium, and is independent of mode. In marked contrast, cylindrical and spherical inclusions have smaller or greater eigenattenuation factors, particularly in lower modes. Under certain conditions of P wave velocity contrast, and Poisson's ratio of the surrounding elastic medium, lower modes have less than 0.1 times the attenuation factor of higher modes. We name these low-attenuation modes (LAMs). LAMs are physically related to the conversion of volumetric changes to shear deformation of the surrounding elastic medium and the radiation of shear waves from the curved boundaries. Some monotonic waveforms of long-period earthquakes can be interpreted by the excitation of these LAMs. Crack modes are also simply formulated by the resonance of a rectangular inclusion and also become LAMs whose attenuation factors are related to the aspect ratio of the crack.