We consider a saddle-point formulation for a sixth-order partial differential equation and its finite element approximation, for two sets of boundary conditions. We follow the Ciarlet-Raviart formulation for the biharmonic problem to formulate our saddle-point problem and the finite element method. The new formulation allows us to use the H 1 -conforming Lagrange finite element spaces to approximate the solution. We prove A priori error estimates for our approach. Numerical results are presented for linear and quadratic finite element methods.Key words. sixth-order problem, higher order partial differential equations, biharmonic problem, mixed finite elements, error estimates.