This paper addresses the circular formation and concentric formation stabilization problem of kinematic unicycles. We design distributed control laws driving unicycles to converge to a common circle at the first stage and a velocity control law enabling unicycles to achieve a specific formation on the circle at the second stage. We also achieve the concentric formation by dividing unicycles into groups and design distributed control laws reinforcing each group at a desired circular orbit from the stationary center. We provide analysis to show that both the circular and concentric formations are asymptotically stable using set stabilization theory. Typical examples are selected to demonstrate and support the theoretical results.