The present paper is to focus on a boundary value problem in a homogeneous, isotropic, elastic body with double porosity. After developing mathematical formulation, a state space approach has been applied to investigate the problem. As an application of the approach, normal force has been taken to illustrate the utility of the approach. The expressions for the components of normal stress and equilibrated stress are obtained in the frequency domain and computed numerically. Numerical simulation is prepared for these quantities and simulated results for these quantities are depicted graphically for a particular model. A particular case of interest is also deduced from the present investigation.