The present invention relates to a shaped solid acid catalyst for the isomerization of hydrocarbons and so on, which has a high activity and is excellent in strength and easily handleable, and processes for the preparation thereof. This catalyst comprises a support comprising portions of zirconia having a tetragonal form and portions of alumina, and a sulfureous component and, if necessary, a Group 8, 9 or 10 metal component both being supported on the support, and has a specific surface area of 150 m2 / g or above. The catalyst can be prepared by kneading aluminum hydroxide, zirconium hydroxide and a sulfureous compound, shaping the kneaded mixture, calcining the shaped material at such a temperature as to form tetragonal zirconia and, if necessary, supporting a Group 8, 9 or 10 metal component on the calcined material and calcining the resulting molding at 300 to 700° C.