For beam passing through cavity mirror twice in multi-pass amplifier laser facility,deformable mirror is often applied at location of cavity mirror for the goal of improving correction range. However,multi-pass amplifier with U-turn for improving optical quality has its own feature different from other facilities. Beam has 90° rotation and size change between 1-2 pass and 3-4 pass propagation. A new mathematical method is described to prove the solution existence of cavity deformable mirror and the application of cavity deformable mirror is verified in Xingguang-Petawatt (XG-PW),facility with U-turn reverser. The results are important for the adaptive optics system design of succeeding large-scale laser facility.