AbstractThe principal co‐ordinates of non‐proportionally damped systems are coupled by non‐zero off‐diagonal elements in the transformed damping matrix. The effects of this damping coupling are investigated, and it is found that significant errors may occur if the dynamic analysis of such systems is based on a truncated set of the overall system modes, even when the damping coupling between these modes is included in the solution. This effect is illustrated by computed results for an idealized soil‐structu