New paradigms for parallel programming have been devised to simplify software development on multi-core processors and many-core graphical processing units (GPU). Despite their obvious benefits, the parallelisation of existing computer programs is not an easy task. In this work, the use of the Open Multiprocessing (OpenMP) and Open Computing Language (OpenCL) frameworks is considered for the parallelisation of the model-based iterative reconstruction algorithm DIRA with the aim to significantly shorten the code's execution time. Selected routines were parallelised using OpenMP and OpenCL libraries; some routines were converted from MATLAB to C and optimised. Parallelisation of the code with the OpenMP was easy and resulted in an overall speedup of 15 on a 16-core computer. Parallelisation with OpenCL was more difficult owing to differences between the central processing unit and GPU architectures. The resulting speedup was substantially lower than the theoretical peak performance of the GPU; the cause was explained.