For the application of Rietveld profile analysis to neutron powder diffraction data a precise knowledge of the peak profile, in both shape and position, is required. The method now in use employs a Gaussian-shaped profile with a semi-empirical asymmetry correction for low-angle peaks. The integrated intensity is taken to be proportional to the classical Lorentz factor calculated for the X-ray case. In this paper an exact expression is given for the peak profile based upon the geometrical dimensions of the diffractometer. It is shown that the asymmetry of observed peaks is well reproduced by this expression. The angular displacement of the experimental profile with respect to the nominal Bragg angle value is larger than expected. Values for the correction to the classical Lorentz factor for the integrated intensity are given. The exact peak profile expression has been incorporated into a Rietveld profile analysis refinement program.