A numerical investigation of depth and current refraction of surface waves for several simple test cases is presented. The refraction scheme is incorporated into a third-generation wave prediction model. It models the effect upon wave propagation of the temporally and spatially varying sea surface elevations and mean currents associated with tides and storm surges. The scheme solves the transport equation for the wave action spectrum. The magnitude of bathymetric depth refraction is large for the lower frequency swell waves. The accuracy to which the proposed scheme can predict refraction is dependent upon the directional resolution of the spectrum. A directional resolution of at least 15¿ is required; the use of a higher directional resolution may be limited by computational resource restrictions. Current refraction effects are very significant for wave propagation across a simple current eddy. Refraction effects are not limited to just a turning of the waves, but also involve significant changes in the spectral shape. Some of the test results exhibit excessive numerical dispersion associated with the use of upwind differencing. The magnitude of this dispersion is much reduced by employing a simple hybrid differencing scheme in wave frequency-direction space. The high degree of numerical dispersion present in the model results is also a result of the nature of the simplified test cases. The magnitude of the numerical dispersion produced by the upwind differencing technique may not be significant when the model is used for storm simulation. ¿ American Geophysical Union 1991