We investigate by numerical simulations the dynamics of alignment of linear molecules in resonant pulsed laser fields and its dependence on pulse length, field strength, and molecular parameters. We propose an analytical short-time approximation for the time-dependent wave packets. We provide a theoretical basis for the occurrence of saturation in the rotational pumping. We present a formula to predict the time at which the maximum alignment occurs. We discuss the magnitude of the laser-induced alignment and we relate it to a theoretical upper limit. (C) 2004 American Institute of Physics.