Recent advances in digitization technologies have transformed the preservation and dissemination of cultural heritage. In this vein, Neural Radiance Fields (NeRF) have emerged as a leading technology for 3D digitization, delivering representations with exceptional realism. However, existing methods struggle to accurately model anisotropic specular surfaces, typically observed, for example, on brushed metals. In this work, we introduce ShinyNeRF, a novel framework capable of handling both isotropic and anisotropic reflections. Our method is capable of jointly estimating surface normals, tangents, specular concentration, and anisotropy magnitudes of an Anisotropic Spherical Gaussian (ASG) distribution, by learning an approximation of the outgoing radiance as an encoded mixture of isotropic von Mises-Fisher (vMF) distributions. Experimental results show that ShinyNeRF not only achieves state-of-the-art performance on digitizing anisotropic specular reflections, but also offers plausible physical interpretations and editing of material properties compared to existing methods.