Symmetric Conservation Laws Mark Hickman Department of Mathematics and Statistics University of Canterbury Christchurch, New Zealand email: M.Hickman@math.canterbury.ac.nz The computation of conservation laws that are "invariant" under a given symmetry is considered. These conservation laws are characterized as eigenfunctions of the prolongation of the symmetry. Under suitable assumptions, the eigenspace for each eigenvalue is finite dimensional and the computation reduces to solving a finite system of linear algebraic equations. These conservation laws are useful in constructing Wahlquist-Estabrook prolongations of the original system of equations (such that the given symmetry extends to the prolongation).