A method of ring artefact suppression in X-ray computerised tomography (CT) reconstructions is proposed. The method is based on the assumption that a sinogram is a smooth function along the horizontal spatial coordinate. Methods based on the theory of ill-posed problems are applied to find a regularised solution. An analytical formula for the solution is proposed allowing fast ring artefact suppression. Its performance is demonstrated for parallel beam synchrotron X-ray tomography.