A strain-based constitutive model, i.e., the mixed stiffness formulation, is presented for a double-porosity material, and coefficients in these linear constitutive equations are identified. All six coefficients are determined by performing properly arranged thought experiments. Three long-time tests are first considered to obtain three independent equations. After that, an experiment to isolate the matrix material from the fracture behavior is performed to provide another four relations. Finally, a case in the long-time limit is considered to identify one of the off-diagonal coefficients in the formulation. In addition, as an example of application of the mixed stiffness formulation, the Navier- type equations are derived for wave propagation problems in double-porosity materials by reformulating the governing equations of some researchers.