Astronomy and Astrophysics, v. 419, p. 1133-1140, 2004. http://dx.doi.org/10.1051/0004-6361:20041093International audienceSolar diameters have been measured from different ground-based instruments on different sites all around the world. There are values dating back to three centuries ago, but the revival of interest began in the 1970s when it was claimed that a temporal periodic modulation had been found. The interest of such measurements, pinpointed from only two decades, may not lie in these temporal variations, but in the fact that a latitudinal heliographic dependence may exist. Such a solar shape distortion has been deduced from the analysis of solar astrolabe data sorted by heliographic latitudes, but observational evidence has also been obtained by means of a scanning heliometer (Pic du Midi Observatory). Latitudinal dependence implies sub-surfacic physical mechanisms and can be explained theoretically. Thus, in spite of the fact that ground-based observations are altered by seeing effects that may amplify or superimpose noise, it can be advanced that the solar shape is not a pure spheroid. We present here a new theory based upon the thermal-wind equation, which explains the observed distorted solar shape. Using the W parameter (called here asphericity-luminosity parameter), we show that large negative values (W ranging from around −0.075 up to −0.6) leading to a prolate Sun, are unlikely. The best range of W lies between around −0.075 and +0.6. Concerning observations, only space missions (or balloon flights) will be able to reach a clear conclusion. A space mission called PICARD is scheduled to be launched by 2008: one of its major aims is to measure these asphericities with astrometric precision