The parallelization of global spectral semi-implicit shallow water models has been studied, with a full three-dimensional primitive equation model in mind. Different strategies have been considered and their scalar stability properties have been analysed. The transposition approach, in which global data transportation is performed between Legendre and Fourier transforms, appears to be most favourable of these strategies, in terms of requiring least bandwith of parallel interconnect to attain prespecified parallel efficiency. Another point in favour of this approach is its simplcity, since all communication in an Eulerian code is concentrated in the global transposition between the spectral forms. The spectral transforms themselves can be carried out independently within individual processors, with the same algorithms that are currently employed on vector supercomputers. A parallel semi-Lagrangian and Eulerian version of a semi-implicit global shallow water model has been implemented using a set of low level macros (PARMACS) to achieve some portability. Benchmark results obtained on an Intel iPCS2 hypercube have been presented, demonstrating the high parallel efficiency of the transposition approach.