The analysis of Lyman α observations in the exosphere of Mars has become limited by the assumption of spherical symmetry in the modeling process, as the models are being used to analyze increasingly detailed measurements. In order to overcome this limitation, a two-dimensional density model is presented, which better emulates the density distribution of deuterium and hydrogen atoms in the exosphere of Mars. A two-dimensional radiative transfer model developed in order to simulate multiple scattering of solar Lyman α photons by an asymmetric, nonisothermal hydrogen exosphere, is also presented here. The models incorporate changes in density and temperature structure of the martian atmosphere with radial distance and solar zenith angle.The 2-D models were applied to the MAVEN-IUVS echelle observations of deuterium and hydrogen Lyman α as well as HST Lyman α observations of hydrogen at Mars. The asymmetric 2-D model provided better fits to the data and smaller thermal escape rates in comparison to the symmetric 1-D model for the exosphere of Mars. However, intensity differences between both models became small above ~2.5 martian radii indicating that the exosphere of Mars approaches spherical symmetry at higher altitudes, in agreement with earlier studies. In addition, a new cross calibration of the absolute sensitivities of two instruments on the Hubble Space Telescope and the MAVEN-IUVS echelle mode is presented based on near-simultaneous observations of the geocorona and Mars.