The topic of this thesis is GPU accelerated sparse linear algebra for subsurface reservoir modeling. Numerical techniques for reservoir sim- ulations are described and we present the open source reservoir simula- tion software toolbox MRST. We discuss some of the challenges related to linear algebra and reservoir simulation. Furthermore, we discuss the possibility GPU-acceleraing the linear algebra for reservoir simulation, and implement a GPU based CG solver preconditioned with AMG for MRST, using the open source linear algebra library CUSP.