- A multilevel recursively defined preconditioner for use with the preconditioned conjugate gradient (PCG) algorithm is developed and applied to solve thin and thick laminated plate problems. The preconditioner is constructed from a sequence of hierarchical vector spaces arising from the p-version of the finite element (FE) method. Numerical studies have been conducted using quadrilateral elements for two-dimensional problems up to p=8 and serendipity brick elements for three-dimensional problems up to p=5. The efficiency of the iterative procedure is illustrated using bending response of laminated plates. The effects of element span ratios, convergence tolerance, polynomial order, material properties, and plate span ratios on the number of iterations required for convergence has been investigated. Results indicate that the preconditioner developed herein can be used to produce an efficient iterative solver for two- and three-dimensional problems in structural mechanics. 2000 Elsevier Science S.A.