We describe the mathematical software package GEOMPACK, which contains standard Fortran 77 routines for the generation of two-dimensional triangular and three-dimensional tetrahedral finite element meshes using efficient geometric algorithms. This package results from our research into mesh generation and geometric algorithms.\parIt contains routines for constructing two- and three-dimensional Delaunay triangulations, decomposing a general polygonal region into simple or convex polygons, constructing the visibility polygon of a simple polygon from a viewpoint, and other geometric algorithms, from which our mesh generation method is built and others can be implemented. Our method generates meshes in polygonal or polyhedral regions specified by their boundary representation and possible interfaces between subregions.