In recent years it has become clear that the vertical structure of disk galaxies is a key ingredient for understanding galaxy evolution. In particular, the presence and structure of extra-planar gas has been a focus of research. The Hydrogen Accretion in LOcal GAlaxieS (HALOGAS) survey aims to provide a census on the rate of cold neutral gas accretion in nearby galaxies as well as a statistically significant set of galaxies that can be investigated for their extra-planar gas properties. In order to better understand the the vertical structure of the neutral hydrogen in the two edge-on HALOGAS galaxies NGC 5023 and UGC 2082 we construct detailed tilted ring models. The addition of distortions resembling arcs or spiral arms significantly improves the fit of the models to these galaxies. In the case of UGC 2082 no vertical gradient in rotational velocity is required in either symmetric models nor non-symmetric models to match the observations. The best fitting model features two arcs of large vertical extent that may be due to accretion. In the case of NGC 5023 a vertical gradient is required in symmetric models (dV/dz =$-14.9\pm3.8$ km s$^{-1}$ kpc$^{-1}$) and its magnitude is significantly lowered when non-symmetric models are considered (dV/dz =$-9.4\pm3.8$ km s$^{-1}$ kpc$^{-1}$). Additionally it is shown that the underlying disk of NGC 5023 can be made symmetric, in all parameters except the warp, in non-symmetric models. In comparison to the "classical" modeling these models fit the data significantly better with a limited addition of free parameters.