This paper presents the application of non-nested and non-structured multigrid methods for two-dimensional elastic linear problems. Some basic aspects related to multigrid methods are discussed including nested iterations, coarse grid correction scheme, transfer operators, and multigrid strategies. A variational formulation for the transfer operators is also considered. The C++ implementation of the multigrid software is discussed and some examples are analyzed. The performance of multigrid strategies is compared with direct and pre-conditioned conjugate gradient algorithms.