Narrow hole bundle structures, whether or not designed for use as sound-absorbing materials and silencers, are frequently observed in catalysts and honeycomb constructions. Being able to make an accurate estimation of the sound-absorption coefficient and transmission loss with respect to such narrow hole bundle structures by using just their dimensions is important. Therefore, in this study, the authors attempted to develop a theoretical estimation method and verified its effectiveness by comparing the results with those of experiments that were performed using two-microphone and four-microphone impedance tubes. Primarily, a propagation constant and the characteristic impedance of sound propagation in a cylindrical narrow tube, which is based on a two-dimensional cylindrical coordinate system analysis including attenuation, was used to perform calculations for precision estimation. Next, an accurate propagation constant and characteristic impedance based on a two-dimensional analysis were converted and introduced to one-dimensional axial coordinate system analysis based on a transfer matrix. The developed method proved to be capable of making an accurate estimation by a simple process using a one-dimensional transfer matrix that is generally used for designing silencers.