The purpose of this work was to identify the relationship between the phase composition and strength of autoclaved pressed stone from a mixture of lime and ash of CHP in the presence of Na2SO4. From these mixtures are made such building materials as silicate brick and blocks from autoclaved cellular concrete. The phase analysis of the autoclaved samples was carried out by X-ray and thermal methods. It was found that the mixtures studied after autoclaving for 8; 50 and 100 hours at 0.8 MPa isotherm with no addition or with 1 and 2% Na2SO4 is represented by gel-like phase C-A-S-H, aluminum substituted tobermorite, hydrogarnet katoite. Adding of 1 and 2% Na2SO4 makes no qualitative change in phase composition, but significantly redistribute the phase composition and increase the rate of phase formation. Thus 2 % Na2SO4 contributes to a substantial increase in the synthesis of Al-tobermorite, but reduces the C-A-S-H phase formation. Katoite hydrogarnet content remains unchanged. The degree of hydration of the composition with 2% Na2SO4 for 8 hours of autoclaving is the same as for 100 hours of treatment without an additive. This increases the strength of the material by 1.65 times with the same 8 hour steaming time. Strength of the stone is always directly proportional to the content of a gel C-A-S-H phase. Its content is proportional to the number of Al-tobermorite in non-additional mixtures, but does not correspond to the content of tobermorite in compositions with addition of 2 % Na2SO4. Keywords: autoclaved building materials, lime-fly ash mixtures, Na2SO4 addition, phase composition, strength of the stone, interrelationships.