Drug screening is an important part of the drug development pipeline for the pharmaceutical industry. Traditional, lab-based methods are increasingly being augmented with computational methods, ranging from simple molecular similarity searches through more complex pharmacophore matching to more computationally intensive approaches, such as molecular docking. The latter simulates the binding of drug molecules to their targets, typically protein molecules. In this work, we describe BUDE, the Bristol University Docking Engine, which has been ported to the OpenCL industry standard parallel programming language in order to exploit the performance of modern many-core processors. Our highly optimized OpenCL implementation of BUDE sustains 1.43 TFLOP/s on a single Nvidia GTX 680 GPU, or 46% of peak performance. BUDE also exploits OpenCL to deliver effective performance portability across a broad spectrum of different computer architectures from different vendors, including GPUs from Nvidia and AMD, Intel’s Xeon Phi and multi-core CPUs with SIMD instruction sets.