We present a method of interpolating multiple arrival traveltimes and amplitudes. It is based on an assumption of the physical continuity of the traveltimes and provides optimal interpolation between adjacent rays using constrained Delaunay triangulation. We use a graphical, interactive program to visualize the data and for quality control. We have developed the algorithms for both the 2-D and 3-D cases, though implemented only the 2-D so far. The method has been tested on several synthetic velocity models and on the SEG-EAGE salt model.