We study the production of spin 3/2 particles in homogeneous scalar and gravitational backgrounds using the mode-mixing Bogolyubov method. Considering only the helicity +/-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 specific supergravity inflationary model and calculate the spectrum of gravitinos created during preheating at the end of inflation.