Abstract: Important engineering applications use unstructured hexahedral meshes for numerical simulations. Hexahedral cells, when compared to tetrahedral ones, tend to be more numerically stable and to require less mesh refinement. However, volume visualization of unstructured hexahedral meshes is challenging due to the trilinear variation of scalar fields inside the cells. The conventional solution consists in subdividing each hexahedral cell into five or six tetrahedra, approximating a trilinear variation by a nonadaptive piecewise linear function. This results in inaccurate images and increases the memory consumption. In this paper, we present an accurate ray-casting volume rendering algorithm for unstructured hexahedral meshes. In order to capture the trilinear variation along the ray, we propose the use of quadrature integration. A set of computational experiments demonstrates that our proposal produces accurate results, with reduced memory footprint. The entire algorithm is implemented on graphics cards, ensuring competitive performance. We also propose a faster approach that, as the tetrahedron subdivision scheme, also approximates the trilinear variation by a piecewise linear function, but in an adaptive and more accurate way, considering the points of minimum and maximum of the scalar function along the ray.