  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 (2018) 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.
