The amplitude and phase of the pressure in the field of a rectangular piston, assumed vibrating within an infinite, rigid baffle, are examined theoretically for ranges down to the order of the piston length. Various laws of behavior of this field, both on and away from the acoustic axis, are deduced. An indication is given of the errors introduced by the approximations used. Such experimental evidence as is available supports the theory. Simple means are provided for constructing curves of axial pressure amplitude and phase for any ratio of length to breadth of the radiating surface, and a method is suggested for predicting the long‐range axial pressure of a rectangular piston from measurements taken well within the latter's Fresnel region. The near fields of a rectangular and a circular piston are compared. That of the rectangular piston produces the more useful approximation to a plane wave.