We use the stochastic rotation dynamics algorithm to investigate the packaging of flexible and semiflexible polymers into a capsid that is permeable to solvent molecules. The model takes into account hydrodynamic interactions arising due to local flow. The flexible chain maintains a random configuration as it is being fed into the capsid, in contrast to the semiflexible chain, whose configuration is initially spool-like, becoming more random at high packing. We measure the packing rate, which is found to decrease with the percentage of the chain packed and highlight the difference between the flexible and semiflexible chains. Reflecting experiments, we find pauses in the packing process for individual chains as the motor loses grip of the fluctuating beads. We also find that hydrodynamics is important, in that the packaging rate is faster when flow is included. (C) 2004 American Institute of Physics.