The divergence of partially coherent flat-topped (PCFT) beams with non circular symmetries in turbulent atmosphere is investigated. Detailed analysis of PCFT beam's divergence demonstrated that elliptical and rectangular symmetries have similar behavior, but PCFT beams with higher order of flatness are more diverged. Also the results show that the PCFT beams with smaller correlation lengths are diverged more than the beams with larger correlation lengths. Increasing the structure constant of turbulent media causes increasing the PCFT beam's divergence. Our results are supposed to be useful in engineer of optical communication systems.