We have developed a new 3-Dimensional numerical solver of the linearized compressible Euler equations (3D GLASS), which we use to model oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh (0 ≤ φ ≤ 2π, 0 ≤ θ ≤ π, 0 ≤ r ≤ R) over a background state generated from the standard Solar Model S. We use a new efficient pseudo-spectral computational method to quickly and accurately calculate the contribution of the compressible material derivative dyad to internal velocity perturbations. The oscillations are computed over arbitrary 3D background velocity fields which can be used to test the effects of theoretical and observational models of internal solar velocities. The goal is to use this algorithm in a “forward-modeling” approach to gain a deeper understanding of data interpreted through helioseismology. To demonstrate the efficacy of this model we show rotational splitting due to solid body rotation as well as the application of local helioseismology techniques to measure the effects of a simple model of single cell meridional circulation.