A numerical model based on the dual reciprocity boundary element method (DRBEM) is presented here for the study of combined wave diffraction and refraction. The model is more general than that presented by Zhu [Zhu S-P. Engng Anal Boundary Elements 1993;12:261–274] in the sense that areas or coastlines where water depth is zero can be dealt with as well. Our comparative study show that the new model is very accurate for long waves (tsunami waves). It is numerically very efficient in comparison with models based on finite elements too. Using the new model, the interaction between the diffraction and refraction effects is examined. It is shown that the diffraction effect is significantly enhanced when there is a combined diffraction and refraction than when there is just diffraction alone.