Based on an essentially different theoretical foundation than common classical diffraction theories that remain in extensive use, this paper discusses from a fresh perspective the theoretical interpretation and prediction of the far-field diffraction of a plane monochromatic wave by a finite periodic array (PA) of identical obstacles. The theoretical treatment rests on the PA extension of the rigorous generalized multiparticle Mie solution (GMM). The truncated periodic structures may have an irregular overall shape with an arbitrary spatial orientation with respect to the incident beam. It is shown that the overall shape and intrinsic geometrical structure of a finite PA play a decisive role in giving rise to an associated far-field diffraction pattern. It is also shown that, when the physical dimensions of individual component units are much smaller than the incident wavelength, the extracted diffraction pattern of a densely packed PA of such small volumes in forward directions exhibits the distinct features predicted from classical diffraction theories for an aperture with the same shape as the overall finite PA. Several typical examples are presented, including two complementary arrays used in the specific discussion concerning Babinet’s principle. There are brief preliminary discussions on some fundamental concepts in connection with the involved theoretical basis and on potential further development and application of the present GMM–PA approach.