Oscillatory current-voltage characteristics of n+-GaAs/semi-insulating Al0.8Ga0.2As/nGaAs heterojunction barriers (400 angstrom thick) grown by molecular beam epitaxy on n+-GaAs (100) substrates are observed at 4 K when the heterostructures are placed under the transverse uniaxial stress along [011] direction (perpendicular to current direction) above 4 kbar. We attribute these oscillations to the resonant indirect Fowler-Nordheim tunneling via [011] oriented transverse X valleys, where the change of wave vector is required for tunneling.