For the understanding of the phonation mechanism and for the design of an artificial vocal cord, we developed a computational method for the fluid-structure interaction, including the elastic walls and membranes. A robust and efficient method is required to deal with large deformation of biological materials and high frequency vibration. To this end, we apply an immersed boundary method. The flow through a two-dimensional channel including a pair of flexible structures, which is a simplification of a vocal cord, is simulated. The elastic solid is modeled by the St. Venant-Kirchhoff constitutive equation and its motion is simulated by a finite-element method, where the contact of the vocal cord is taken into account by a Lagrange multiplier method. The incompressible fluid flow is computed by a finite-difference method. Then the immersed-boundary method of a body-force type developed by the authors is successfully applied for the fluid-structure interaction. In the present results, the deformation of the structure and the frequency of the pulsating flow are reasonably reproduced. The obtained frequency is within the measured range of the data for a human vocal cord. Also, two velocity peaks are observed when the vocal cord is in the opening and closing phases in each period of the vocal cord vibration, and the velocity of the closing phase is larger than that of the opening phase.