Let R be a commutative ring with identity 1 ≠ 0 and T be the ring of all n × n upper triangular matrices over R. In this paper, we describe the zero divisor graph of T. Some basic graph theory properties of are given, including determination of the girth and diameter. The structure of is discussed, and bounds for the number of edges are given. In the case that R is a finite integral domain and n = 2, the structure of is fully described and an explicit formula for the number of edges is given.