  We study the production of gravitinos during the preheating era after
inflation by means of the non-perturbative Bogolyubov technique. Considering
only the helicity $\pm 3/2$ states, the problem is reduced to the simpler Dirac
fermions case. We calculate the production in a particular supergravity model
in an expanding universe and obtain the spectrum and number density. Finally we
compare the results with the nucleosynthesis bounds and extract some
consequences.
