This paper investigates the three dimensional (3-D) spatial correlation characteristics of uniform concentric ring arrays (UCRAs) deployed in antenna systems. Closed-form formulas of the 3-D spatial correlation functions are derived. UCRAs with two different geometric structures and uniform distribution angular energy distribution are considered. It is found that the 3-D spatial correlation is a function of antenna sensor spacing, the geometric structure of a UCRA. Simulation results are presented for illustration and comparison.