Generalized analytic functions can be used to study 2d problems of applied mathematics. In general such a treatment bases on function-theoretical methods as Cauchy type integral formula, series representations or the study of integral equations. The present paper is devoted to the study of axially symmetric Oseen models for viscous incompressible fluids by the theory of generalized analytic functions. As a first step some theoretical results are proved for so-called \(H\)-analytic functions for special geometries. These results are used for treating Oseen equations. Here, one goal is to derive integral representations of model sizes as velocity, pressure and vorticity by the aid of these generalized analytic functions. Another goal is to derive integral equations for the solutions which can be treated by numerical methods. The obtained integral equations are compared with the known Oseenlet-based integral equations, not only from the analytical point of view but also from the view of numerical or computational treatment.