The unsteady fluid-dynamic forces, generated by a flexural motion in axial (laminar) flow, have been formulated based on a collocation finite-difference method for concentric configurations, in connection with the flow-induced vibration problem. Based on the numerical method, the governing equations of the unsteady flow, obtained from the appropriate Navier-Stokes and continuity equations, redcuced to a system of algebraic equations leading to a block-tridiagonal system. To obtain a solution of the system, the LU decomposition method is used considering the factorization scheme. This numerical method is capable of taking fully into account unsteady viscous effects and of predicting viscous forces rigorously rather than approximately, in contrast with existing theories. In order to validate the numerical approach, semi-analytical approaches have been developed for estimating the fluid-dynamic forces. The numerical results are compared to the analytical results and good agreement was found. The contribution of unsteady viscous damping forces to the overall unsteady forces is significant for low values of the oscillatory Reynolds number, expecially in very narrow annuli.