In this paper, a computational model is presented for the solution of wave-current
interaction problems. At first, we derive two series of governing equations, current equations
and wave equations. The numerical solution of the governing equations is carried out at two
levels, viz. a wave level and a current level. In the wave level calculation, the current field
is known and the wave ray paths are determined through step by step integration of a set of
differential equations. In each step of integration, the equation of the wave action conservation
and the wave number conservation are solved to determine wave height and wave
number, respectively. In the current level, the characteristics of wave are known, and the
governing equations of the shallow water are solved by Galerkin FINITE ELEMENT method and
the current unknowns (velocity and depth) are determined. The calculations are initiated in a
wave phase, where currents are neglected. The two-level iterative model is continued until the
results are converged. Based on this method, two computer programs called "SWERM" and
"CAFEM" are developed in FORTRAN 77. Several examples are run by programs and the
results are presented. The results show that, when the current has a positive component in the
direction of wave propagation, the wave length increases and the wave height decreases.
Conversely, a negative current component reduces the wave length and increases the wave
height. Also, for a current in the direction of the wave, current velocity increases. The results are
compared with the cited results and the accuracy of results is checked.