Forces that a tsunami exerts on a concrete girder bridge have been evaluated by a Computational Fluid Dynamics (CFD) method and a possible mechanism is examined that may have been responsible for damages of typical small road bridges observed after the tsunami resulted from the Great East Japan Earthquake of 2011. The CFD method employed is a fully three-dimensional Large Eddy Simulation (LES) method that allowed a detailed examination of time-resolved changes of magnitudes of the horizontal and vertical forces and the moment forces including the buoyancy effects. A typical 8m wide four-girder bridge is found to experience a moment force that is large enough to push the seaward edge of a bridge deck upwards when the tsunami comes with a bore of one to two meters. It is consistent with the indication of survey results of several damaged bridges.