In this paper we take a first step toward the development of a realistic global magnetospheric model in which the magnetic forces are equilibrated by plasma pressure forces. Such a model describes a quasi-static equilibrium, a condition valid at most times in the Earth's magnetosphere. The work reported here involves the coupling in two dimensions of a numerical inner/middle magnetosphere model in flux coordinates, which solves the Grad-Shafranov equation in inverse form, with an asymptotic magnetotail model farther away from Earth. We discuss the obtained configurations (including the resulting magnetic fields and electric currents) under different observation-based inputs (parameters include plasma and total pressures, as well as the magnetic flux boundary). In particular, we focus on the boundary value problem, in which we take realistic shapes for the outer magnetic flux surface (close to the magnetopause) and plasma pressure distributions as model inputs and obtain the total pressure variation in the tail as a by-product of the model.