X-ray reflection spectroscopy is a powerful tool for probing the strong gravity region of black holes and can be used for testing general relativity in the strong field regime. Simplifications of the available relativistic reflection models limit the capability of performing accurate measurements of the properties of black holes. In this paper, we present an extension of the model relxill_nk in which the accretion disk has a finite thickness rather than being infinitesimally thin. We employ the accretion disk geometry proposed by Taylor & Reynolds and we construct relativistic reflection models for different values of the mass accretion rate of the black hole. We apply the new model to high-quality Suzaku data of the X-ray binary GRS 1915+105 to explore the impact of the thickness of the disk on tests of the Kerr metric
