<p>As a universal theorem of linear physical systems, reciprocity theorems describe the reciprocity relation between the input and output of linear systems. In the context of the linearized elasticity theory, different types of the reciprocity theorem are investigated in a comprehensive manner for elastic waves propagating in a solid medium. A rigorous derivation is presented and discussed for the equations of reciprocity theorems in the time domain, the frequency domain, the time-convolution type and the frequency-power type. In addition, more generalized reciprocity theorems assuming the piezoelectricity of some solid materials are also presented, which allow for the coupling effect of elastic waves and electromagnetic waves. The results obtained in this work can not only complete the reciprocity theory of linear elastodynamics, but also provide theoretical guidance for practical applications in engineering and applied physics.</p>