Gd-doped ceria fluorites (CGO) exhibits prominent electro-chemo-mechanical properties and giant-electrostriction at room temperature has been recently disclosed in both CGO polycrystalline films and bulk. Such electromechanical properties depend on oxygen vacancy defects in the fluorite lattice and early experiments suggest that defects along the  crystallographic direction promote high atomic distortion, resulting in the largest electrostriction response. However, only out-of-plane electrostriction (i.e. M13) in (111) CGO oriented thin films has been reported so far and several questions remain open about electrostriction mechanism in the oxygen defective fluorite. Here, we present electromechanical performances along with different crystallographic directions. We grow thin films by pulsed laser deposition on single crystals substrates to obtain longitudinal and shear deformations (i.e. M11 and M12) of highly coherent (100), (110) and (111) oriented CGO thin films. As a result, we find an order of magnitude higher electrostrictive coefficient along , resulting in a new insight into the mechanism of CGO electrostriction.