The propagation of a Ni_like Ag x_ray laser operating at 139 nm is numerically simulated. A two_dimensional ray tracing code is used to investigate the refraction and saturation effects of the x_ray laser beam as a postprocessor of a one_dimensional hydrodynamic code. The x_ray laser beam trajectory in a plasma medium and the spatially integrated laser output intensity as functions of the plasma length are calculated. Numerical results show that the refraction effect plays an important role in the beam propagation and amplification process.