In the present study, Fast and accurate algorithms for the generation of contour surfaces in 3D are described using hexahedral elements which are popular in finite element analysis. The contour surfaces are described in the form of groups of boundaries of contour segments and their interior points are derived using the contour equation. The locations of contour boundaries and the interior points on contour surfaces are as accurate as the interpolation results obtained by hexahedral elements and thus there are no discrepancies between the analysis and visualization results.