The Laplace-Beltrami equation on a hypersurface \(T \subset \mathbb R^{n+1}\) is solved when \(T\) is given as a zero level set of a function \(\Phi\). In particular, \(T\) may be a complicated surface. The differential equation is extended to a band of thickness \(h\) in \(\mathbb R^{n+1}\) around the surface, and a finite element method is used on a mesh of the band. It is not assumed that the finite element mesh is aligned to the surface. Error estimates and numerical results are provided for a Poisson equation.