Flexible structures used in devices, such as micro/nano resonators, sensors, etc. are subjected to fluid forces. Estimation of damping coefficient due to the fluid forces in flexible structures is of utmost importance for the designs of these structures. In existing literatures, empirical correlation for the estimation of damping coefficient are available for the non-flexible structures only. Therefore, development of, preferably simple, analytical method of estimation of damping coefficient in flexible structures subjected to various mode shapes. In this work we attempt to develop such a model from the first principle. The results of the model are validated with the data available for non-flexible structure. Analysis of three mode shapes is performed using the analytical model and the results are compared with the numerical data. Computations are conducted using the finite difference method-based IB2d fluid–structure interaction solver, which solves Navier-Stokes equation for fluid-region using the Eulerian and an equation of motion for solid-region using the Lagrangian approach. A connectivity between fluid and structure is made through a forcing function which is a source term in the momentum equation. From the numerical simulations the average damping coefficients respectively, for first, second and third mode shape are found to be 0.79×10-3, 1.49×10-3, and 2.01×10-3. It is concluded that, with the given flow velocity (low Re), reasonable predictions of damping coefficients can be made using the proposed analytical model for the flexible structures.