FAST linear accelerator has been commissioned in 2017. Experimental program of the facility requires high quality beams with well-defined properties. Solenoidal fields at photoinjector, laser spot shape, space charge forces and other effects can distort beam distribution and introduce coupling. This work presents results of a beam phase space tomography for a coupled 4D case. Beam was rotated in two planes with seven quads by 180 degrees and images from YaG screen were used to perform SVD based reconstruction of the beam distribution.