Two approaches for testing hexagonally connected systolic arrays are presented. The first one gives general testability conditions for such arrays. Under these conditions, hexagonal systolic arrays can be tested with a test set that increases linearly with the number of cells. For an array of MN cells, the testing procedure can be completed in a linear number of time units. The second approach gives stronger conditions and a simpler test procedure. Under these conditions, hexagonal systolic arrays can be tested with a constant number of distinct test vectors independent of the array size and in a number of time units that varies with max(M, N). It is shown that hexagonally connected systolic arrays that are used for matrix multiplication satisfy the second set of conditions and can be tested with a simple test procedure.