The effect of specimen surface curvature on profiles of asymmetric X-ray diffraction peaks obtained using the Bragg-Brentano geometry with a position sensitive detector (PSD) was studied. Asymmetric diffraction peaks were experimentally obtained from cylindrical surfaces with controlled curvature. Peaks were collected for a set of curvature radii, diffraction angles, and materials. A mathematical approach and a computer model for calculations of peak profiles were developed: a general method for computation of peak profiles is consideration of diffraction cones intersection with the PSD surface. Effects of axial and radial divergence, finite sample size, and local surface tilt were included in the model. Calculated peak profiles agree with reflections obtained experimentally at a wide range of curvature radii and diffraction angle values. Computation of important characteristics such as the peak centroid and change in position of the maximum and full-width-half-maximum is provided.