We propose an improvement to the dynamic oscillation method using as an example the measurement of the tensile stiffness of the rabbit tracheal mucosal membrane. A sine wave oscillation technique was used to study the tissue mechanical properties. A mathematical model was developed using fast Fourier analysis. After mathematically eliminating the machine response, this analysis reveals the tissue frequency response over a wide range of frequencies. This study addresses the advantages of using Fourier analysis to interpret dynamic properties of biological tissue and provides a complete description of how to obtain the pure tissue response.