We study the production of spin 3/2 particles in homogeneous scalar and gravitational backgrounds from the mode-mixing Bogolyubov method. Considering only helicity $\pm 3/2$ states we can reduce the problem to a standard Dirac fermion calculation and apply the standard techniques in a straightforward way. As an example we consider a supergravity inflationary model and calculate the spectrum of gravitinos created during preheating at the end of inflation.