This paper is concerned with the implementation of parallel iterative methods for solving large sparse symmetric positive definite linear systems arising form finite difference methods, Ax=b, on an SIMD computer, the CM-2. Specifically, we are interested in the Conjugate Gradient (CG) method introduced by Hestenes and Stiefel. This method is a popular method and effective linear systems solver, notably when combine with a preconditioner, one attractive possibility considered by Ashby or Ciarlet, Meurant, Perlot or Freud or Johnson, Mitchell and Paul is polynomial preconditioning. Its main advantage is its suitability for vector and/or parallel computers, when the matrix by vector product is parallelizable. Whenever A has a regular sparsity structure (multidiagonal), polynomial preconditioning is effective on parallel machine.