In a process for making calcium sulfate hemihydrate suitable for a construction material from a moist finely divided gypsum obtained by flue gas desulfurization from a power plant fired by brown coal, the improvement wherein a molded body is formed by pressing said gypsum at a pressure from 0.1 to 14 N/mm.sup.2, said gypsum having physically bound water in a range from about 3 to 20% by weight, said pressing being sufficient to achieve 15 to 60% pore volume and more than 5% of said pore volume containing air, said molded body being fed at ambient temperature to an autoclave and being heated in said autoclave with saturated steam, water being formed by condensation of said saturated steam and subsequently being drawn into said molded body as a condensate by capillary action of said pores, water held in said pores at least partially coming from said finely divided gypsum from which said molded body is formed, regulating crystal growth and crystal pattern of calcium sulfate hemihydrate growing from an aqueous solution phase by control of a process temperature in the range between 110.degree. C. and 180.degree. C. and by the pressure of the process atmosphere in said autoclave, said pressure being at or above that of saturated steam at said process temperature, after said growth at least partially forcing out said water present in said pore volume of said molded body by controlled release of said pressure in said autoclave, and said molded body being removed from said autoclave.