Equilibria of axially moving beams transversely and longitudinally coupled with the fixed boundary conditions are numerically studied in the supercritical transport speed ranges. In the supercritical regime, the pattern of equilibria consists of the straight configuration and of non-trivial solutions that bifurcate with transport speed. The numerical schemes are presented for the governing equation of coupled planar and the corresponding static equilibrium equation for non-trivial equilibrium solutions via the finite difference method under the fixed boundary conditions. A copper beam is treated as example to demonstrate the non-trivial equilibrium solutions. Numerical results indicate that the equilibrium of the coupled planar with the changing parameters.