AbstractThe usual assessment of performance of Newmark's method for direct integration in structural dynamics is by reference to amplitude and period error of a single mode of vibration. As an alternative the local and global truncation errors due to the time discretization are introduced. Methods of obtaining norms of the error sequences are presented. The results of numerical experiments confirm the anticipated error order and show how the error formula varies with β. The effect of the presence of physical damping on the error order and formula is also examined