  On an affine variety $X$ defined by homogeneous polynomials, every line in
the tangent cone of $X$ is a subvariety of $X$. However there are many other
germs of analytic varieties which are not of cone type but contain ``lines''
passing through the origin. In this paper, we give a method to determine the
existence and the ``number'' of such lines on non-degenerate surface
singualrities.
