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The Finite Element Method (FEM) has proved to be an important technique in machine tool structural analysis. However, the preparation and computing time and cost required for an FEM analysis has constrained the wide application of the method. The Boundary Integral Equation (BIE) method eliminates some of the disadvantage and has consequently replaced the FEM in many fields. In this investigation a BIE program is used to solve two structural problems relevant to machine tools. The results are compared with finite element solutions and it is found that for the same level of accuracy the BIE approach involves less time and cost. A machine tool bed is discretised for both FE and BIE methods. The resulting meshes are compared and advantages and disadvantages of the two methods discussed.