It is demonstrated theoretically that the characteristic wave u-c of shallow water equations is splitted into two waves on the erodible bed with the bed deformation. Such behaviors of the waves eliminate the flow analysis problem at Fr=1. The results of the theory are applied to the three types of numerical calculations using FDS method. 1. Rigorous calculations of the bed deformation; For Fr<1, main bed wave propagates downstream and reverse for Fr>1. 2. Flow calculation without bed deformation; Flow including the point Fr=1 is calculated successfully without any adjustment of the control section problem. 3. Simplyfied version of the bed analysis; The traditional way is modified in which the efficiency of calculation is more compared to the rigourous method.