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The paper gives a bibliographical review of finite element methods(FEMs) applied for the analysis of pressure vessel structures/components and piping from the theoretical as well as practical points of view. This bibliography is a new addendum to the Finite elements in the analysis of pressure vessels and piping - a bibliography [1-3]. The listings at the end of the paper contain 856 references to papers and conference proceedings on the subject that were published in 2001-2004. These are classified in the following categories: linear and nonlinear, static and dynamic, stress and deflection analyses, stability problems, thermal problems, fracture mechanics problems, contact problems, fluid-structure interaction problems, manufacturing of pipes and tubes, welded pipes and pressure vessel components, development of special finite elements for pressure vessels and pipes, finite element software, and other topics.