Aims.We use spectro-polarimetric THEMIS/MSDP data to investigate the 3D structure of solar magnetic-flux tubes across the upper photosphere. Methods. Profiles of the sodium D1 line 589.6 nm are analysed by the bisector method at different wavelengths from the core to the wings, for several bright features. They are compared to synthetic profiles derived from 2D magnetic models of flux tubes and from the MULTI code for NLTE line profiles. Three different magnetic models of flux tubes are investigated. Model (I) consists of a single flux tube that compensates for the horizontal Lorentz forces exactly, while model (II) uses a compromise between horizontal and vertical components. Model (III), a conglomerate of thinner flux tubes, leads to the best agreement with observations. Results. (1) The combination of seeing effects (small filling factor) with slopes of line profiles, which are different in the flux tubes and the neighbouring quiet sun, account for the decrease in observed magnetic field from line core to line wings in central parts of magnetic features, as well as the decrease in magnetic fluxes integrated over the whole magnetic features. (2) The expansion with height of single magnetic flux tubes (models I and II) accounts for the increase in the size of magnetic features from line wings to line core. (3) Pure thermodynamical criteria characterising Dopplershifts and line-intensity fluctuations of magnetic and non-magnetic features have been proven by observations. Conclusions. We could account for differential Zeeman effects along the D1 line profile by combining expansion of flux tubes with height, low gas pressure inside flux tubes, and small filling factor due to seeing effects. Better agreement with observations, in particular with respect to magnetic field amplitudes, will probably need 3D models that take velocity fields and horizontal gradients of temperature into account.