The linearized sound field of a baffled piston source (radiusa, wavenumberk) in a dissipative fluid is considered. A simplified parabolic equation is derived forka≫1 and then solved analytically. The solution matches a plane collimated beam in the vicinity of the source and has the Bessel function directivity in the farfield. The nearfield–farfield transition is studied. The range of validity of the parabolic equation is discussed. Its exact solution is shown to be the first term of an expansion in powers of (ka)−2for the solution of the Helmholtz equation. The higher‐order terms are secular at distances of ordera(ka)1/3from the piston.