Due to their low Young's Modulus, high strength and suitability for additive manufacturing, non-toxic beta-type titanium alloys are emerging as next-generation biomaterials. We present novel experimental results that demonstrate significant variation of Young's Modulus with direction for selective laser melted (SLM) biocompatible Ti-24Nb-4Zr-8Sn (Ti2448). Grain orientation data for SLM-processed Ti2448 is measured using electron backscatter diffraction. By assuming the grain orientations are fixed relative to the axes of the SLM build machine, the measured grain orientation data is used to generate a detailed microstructural finite element model of the polycrystalline SLM-processed material. The computational model provides excellent predictions of the anisotropic properties of SLM-processed Ti2448, indicating that preferential grain orientations that form during SLM processing of Ti2448 cause the experimentally measured variation of the Young's Modulus. The results show that computational models are able to accurately predict the anisotropic Young's Modulus of polycrystalline materials, and, in the context of biocompatible Ti2448 show how to tailor the modulus of SLM components by choosing the build orientation.