The present paper gives a comparative evaluation of two approaches to the determination of the homogeneous nucleation rate in molecular dynamics computer experiments, viz, the methods of the mean lifetime of a metastable system and the mean time of the first passage to a cluster of a prescribed size. The crystal nucleation rate in a supercooled Lennard-Jones liquid has been determined in molecular dynamics simulation as a function of pressure at a reduced temperature T* = 0.55. The results of simulation have been compared with classical homogeneous nucleation theory. Good agreement between theory and the results of computer simulation has been found. (C) 2011 Elsevier B.V. All rights reserved.