This paper presents the optimization results of synthesis conditions of 1,3,5, 7-tetranitro-1 ,3,5, 7-tetraazacyclooctane (HMX) according to modified Bachmann method. The ranges of variables were: hexamine (0.29-0.43 mol), nitric acid 99.5 percent (1.67-2.13 mol), ammonium nitrate (1.20-1.52 mol), paraformaldehyde (0.04-0.10 mol) and acetic anhydride (3.16-3.52 mol). The constant parameters were: temperature (44 +/- 2)°C, reaction time (1st and 2nd dosing-time: 30 minutes, 1st aging-time or