SHAP (SHapley Additive exPlanation) values provide a game theoretic interpretation of the predictions of machine learning models based on Shapley values. While exact calculation of SHAP values is computationally intractable in general, a recursive polynomial-time algorithm called TreeShap is available for decision tree models. However, despite its polynomial time complexity, TreeShap can become a significant bottleneck in practical machine learning pipelines when applied to large decision tree ensembles. Unfortunately, the complicated TreeShap algorithm is difficult to map to hardware accelerators such as GPUs. In this work, we present GPUTreeShap, a reformulated TreeShap algorithm suitable for massively parallel computation on graphics processing units. Our approach first preprocesses each decision tree to isolate variable sized sub-problems from the original recursive algorithm, then solves a bin packing problem, and finally maps sub-problems to single-instruction, multiple-thread (SIMT) tasks for parallel execution with specialised hardware instructions. With a single NVIDIA Tesla V100-32 GPU, we achieve speedups of up to 19x for SHAP values, and speedups of up to 340x for SHAP interaction values, over a state-of-the-art multi-core CPU implementation executed on two 20-core Xeon E5-2698 v4 2.2 GHz CPUs. We also experiment with multi-GPU computing using eight V100 GPUs, demonstrating throughput of 1.2M rows per second -- equivalent CPU-based performance is estimated to require 6850 CPU cores.