The effect of Ba content on the stress sensitivity of the antiferroelectric to ferroelectric phase transition in (Pb_0.94−xLa_0.04Ba_x)[(Zr_0.60Sn_0.40)_0.84Ti_0.16]O₃ ceramics is investigated through monitoring electric field-induced polarization and longitudinal strain under compressive prestresses. It is found that incorporation of Ba significantly suppresses the stress sensitivity of the phase transition, as manifested by slight decreases under prestresses up to 100 MPa in the maximum polarization (P_m) and longitudinal strain (x_m). The energy storage density is even increased under the mechanical confinement in compositions x = 0.02 and 0.04. X-ray diffraction, transmission electron microscopy, and dielectric measurements indicate that the suppressed stress sensitivity is associated with the disruption of micrometersized antiferroelectric domains into nanodomains and the transition from antiferroelectric to relaxor behavior.