Arrays of truncated circular cylinders are the main components of many offshore floating structures. Most analyses on the hydrodynamic interactions among cylinders for such cylinder groups usually considered the instance that cylinder arrays react to loads as one whole body, namely that there is no relative position variations between each cylinder of the arrays. Such analysis is not applicable for the case that there are relative motions among cylinders. Then the method of eigenfunction expansion was used to study the hydrodynamic interactions among truncated circular cylinders. The radiation and diffraction by truncated cylinders in which each cylinder performing surge, sway and heave motions with different amplitudes are analyzed. The velocity potential is obtained. After degenerate case comparisons, hydrodynamic forces and pressure distributions are calculated for more complicated cases, in which multi-cylinders perform different mode oscillations with different amplitudes simultaneously.