In this paper we present a new method for lossy compression of volumetric data that is based on data dependent triangulation. We have extended an approach that has previously been successfully applied in the case of two dimensional images. In our method we first select significant points in the data, and using them, a three dimensional Delaunay triangulation is created. The tetrahedrons existing in the triangulation are used as cells for a linear interpolation spline that gives an approximation of the original image. The compression is done by storing the positions and values of the nodes of the tetrahedrons instead of the entire data set. We compare our compression technique to JPG 2000 3D which is a de-facto standard for compression of volumetric data. Tests are done on different classes of data sets, on which we compare the bits per voxel needed to achieve the same level of peak signal to noise ration. We show that our algorithm performs significantly different than wavelet based compression, as in the implementation of JPG 2000 3D, and in case of data that is smooth outperforms it.