||2.We consider the forced Burgers equation, where the forcing term is Z^2-periodic. Our problem is to find $Z^2$-periodic (weak) solutions of the equation in a constructive way. First, I talk about the connection between the forced Burgers equation and Hamiltonian systems: One of the central issues in the theory of Hamiltonian systems is to look for their invariant manifolds. The graph of Z^2-periodic solution to the forced Burgers equation plays an important role in the issue. Second, I show convergence proofs and numerical simulations to two methods of constructing Z^2-periodic solutions: The one is based on the long time behavior of Lax-Friedrichs difference scheme. The other is based on the Newton’s methods, regarding Z^2-periodic solutions as fixed points of the Poincare map.