This paper presents the finite element method for the analysis of the short wave problem expressed by the Boussinesq equation which considers the effect of wave crest curvature. The standard Galerkin finite element method is employed for the spatial discretization using the triangular finite element based on the linear interpolation function. The combination of the explicit and the quasi-explicit schemes, i.e. the explicit scheme for ihe continuum equation and the quasi-explicit scheme for the momentum equation, is employed for the discretization in time. To show the applicability of the present method for the practical problem, the simulation of wave propagation in one-dimensional and two-dimensional channel flows are carried out. The numerical results are in good agreement with the experimental results being performed previously, The practical example applied to Miyako Bay is presented.