This work presents resequencing techniques for minimizing bandwidth, profile and wavefront of finite element meshes. A unified approach relating a finite element mesh, its associated graphs, and the corresponding matrices is proposed. The geometrical information available from conventional finite element program is also used in order to improve heuristic algorithms. Following these ideas, the algorithms are classified here as a nodal graph (G), a dual graph (G) or a communication graph (G.) associated with a generic finie element mesh. The most widely used topological algorithms, such as Reverse-Cuthill-McKee (RCM), Collins, Gibbs-Poole-Stockmeyer (GPS), Gibbs-King (GK), Snay, and Sloan, are investigated in detail. In particular, the Collins algorithm is extended to consider nonconnected components in associated graph and the ordering provide by this algorithm is reverted for improved profile. This new version is called Modified Reverse Collins (MRCollins). A purely geometrical algorithm, called Coordinate Based Bandwidth and Profile Reduction (CBBPR), is presented. A new hybrid reordering algorithm (HybWP) for wavefront and profile reduction is proposed. The Laplacian matrix [L(G), L(G) or L(G.)], used for the study of spectral properties of an FEG, is constructed from usual vertex and edge conectivities of a graph. An automatic algorithm, based on spectral properties of an FEG, is proposed to reorder the nodes and/or elements of the associated finite element meshes. The new algorithm, called Spectral FEG Resequencing (SFR), uses global information in the graph; it does not depende on a pseudoperipheral vertex in the resequencing process; and it does not use any kind of level structure of the graph. A new spectral algorithm for finding pseudoperipheral vertices in graphs is also proposed. The algorithmpresented herein are computationally implemented and tested against several numerical examples. Finally, conclusions are drawn and directions for futue work are given.