The propagation of solar Alfvén waves in interplanetary space is studied in the approximation of geometrical optics. Ray paths and the change of wave vectors and amplitudes along the rays are determined assuming an Archimedean-spiral interplanetary magnetic field. In particular, the Alfvénic fluctuations in the 2 directions perpendicular to the magnetic field direction are calculated under the assumption that the Alfvén waves are produced at the Sun and emitted with an isotropic directional distribution from a reference level close to the Sun. It turns out that due to the combined effect of spherical expansion of the solar wind flow and the spiralling of the interplanetary field the magnetic fluctuations in the direction perpendicular both to the unperturbed field and the radial direction have much more power than in the other directions (directional anisotropy). Our results are compared with spacecraft observations made by Belcher and Davis (1971), that show an anisotropy of a similar character. It is argued that under average conditions the physical process leading to an anisotropy is not selective coupling of Alfvén waves into compressional waves, as suggested by Belcher and Davis, but rather the above mentioned dissipationfree effect of geometrical optics. Finally, arguments are presented to explain the discrepancy between the calculated high anisotropy and the measured low anisotropy in terms of finite amplitude effects and wavescattering.