We show that piezoelectric effects can give rise to internal electric fields that modify the current-voltage characteristics of double barrier resonant tunneling devices, if suitable stresses are applied. Electric polarization fields in the direction perpendicular to the interfaces arise in heterostructures on (001)-oriented substrates under uniaxial stress parallel to the (110) or (11̄0) orientations. We measured current-voltage characteristics of (001)-oriented AlAs/GaAs/AlAs double barrier structures as a function of uniaxial external stress applied parallel to the (110) and the (11̄0) orientations. The substrate contact was grounded in all measurements. Under (110) stress, the resonance peaks shift to more positive voltages for both positive and negative bias. For (11̄0) stress, the peaks shift toward more negative voltages. We also calculated the current-voltage characteristics of resonant tunneling structures under uniaxial stress, taking into account stress effects on the band alignment and piezoelectric effects. We obtain satisfactory agreement between our calculations which contain no adjusted parameters and the measured data.