We performed molecular dynamics simulations of the genome packaging of bacteriophage P4 using two coarse-grained models of DNA. The first model, 1DNA6 (one pseudo-atom per six DNA basepairs), represents DNA as a string of beads, for which DNA torsions are undefined. The second model, 3DNA6 (three pseudo-atoms per six DNA basepairs), represents DNA as a series of base planes with torsions defined by the angles between successive planes. Bacteriophage P4 was packaged with 1DNA6, 3DNA6 in a torsionally relaxed state, and 3DNA6 in a torsionally strained state. We observed good agreement between the packed conformation of 1DNA6 and the packed conformations of 3DNA6. The free energies of packaging were in agreement, as well. Our results suggest that DNA torsions can be omitted from coarse-grained bacteriophage packaging simulations without significantly altering the DNA conformations or free energies of packaging that the simulations predict.