We present an algorithm to efficiently compute accurate volumes and surface areas of macromolecules on graphical processing unit (GPU) devices using an analytic model which represents atomic volumes by continuous Gaussian densities. The volume of the molecule is expressed by means of the inclusion-exclusion formula, which is based on the summation of overlap integrals among multiple atomic densities. The surface area of the molecule is obtained by differentiation of the molecular volume with respect to atomic radii. The many-body nature of the model makes a port to GPU devices challenging. To our knowledge, this is the first reported full implementation of this model on GPU hardware. To accomplish this, we have used recursive strategies to construct the tree of overlaps and to accumulate volumes and their gradients on the tree data structures so as to minimize memory contention. The algorithm is used in the formulation of a surface area-based non-polar implicit solvent model implemented as an open source plug-in (named GaussVol) for the popular OpenMM library for molecular mechanics modeling. GaussVol is 50 to 100 times faster than our best optimized implementation for the CPUs, achieving speeds in excess of 100 ns/day with 1 fs time-step for protein-sized systems on commodity GPUs. (C) 2017 Wiley Periodicals, Inc.