A multigrid algorithm is described that can be used to obtain the finite element solution oflinear elastic solid mechanics problems. The method is applied to some two dimensional problems to evaluate its strengths and weaknesses. Extensive studies are made to determine the convergence behaviour of the method. In general, this depends on many factors: the number of degrees-of-freedom in the discretization, characteristics of the algorithm, Poisson's ratio when it is close to 0.5, the amount of bending deformation in the problem under consideration, and the degree of non-uniformity in the mesh. Only certain values of the multigrid parameters allow a converged solution to be obtained with a computational effort proportional to the number of degrees-of-freedom. These values include the optimum ones, i.e. those that lead to convergence with the least computational effort. The constant of proportionality is only independent of the number of degrees-of-freedom and still depends on the other factors listed above.

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