The Monte Carlo method has been applied to the calculation of the energy flux of scattered gamma radiation in a spherical room surrounded by an infinitely thick spherical wall and with a point source at the center. Source energies were 1, 2, 4, 6, and 10 Mev. The main investigation was carried out at a room radius of 500 cm but, for the 1 Mev source, the influence of varying the room radius down to 1 cm was analyzed. The results contain energy distributions of the first four successive reflection components at the center of the room and at the wall surface, as well as spatial distributions of the successive energy flux components. The neglect of reflection contributions of order five and higher was estimated to introduce an error of less than 0.2% of the total scattered energy flux. An analytical approximation is shown to produce a useful and easily applicable method of predicting the amount of scattered radiation in a spherical room.