A boundary diffraction wave (BDW) formulation is developed for predicting the collective radiation from large finite planar phased array antennas in a relatively efficient manner. This collective radiation is described in terms of a set of Floquet waves (FWs) arising from the array interior, together with the diffraction of these FWs by the finite array element truncation boundary; the latter is represented by a line integral of the incremental diffracted field over this boundary. In general, the BDW line integral must be evaluated numerically. The current distribution over the whole array is first obtained, for a given excitation, by full wave numerical methods. A traveling wave expansion is employed to represent the array distribution so as to facilitate the development of the BDW solution for arrays. Some numerical results based on the BDW are presented to demonstrate the utility and accuracy of the method for analyzing large planar arrays.