Recent satellite measurements of the solar total irradiance (S) indicate that on time scales of days to months the solar constant varies by a few tenths of a percent. The predominant part of these variations can be explained by blocking of the upward solar flux by sunspots. The observations are consistent with current theoretical models of energy storage in which the energy blocked by the sunspots is temporarily stored in the convective zone. We present modelled solar constant variations on a day by day basis selected from model calculations for the period 1874 through 1981 (Hoyt and Eddy, 1982). Because neither faculae nor bright rings about sunspots balance the net blocking by sunspots, there is a net eleven year modulation in irradiance with a relative depression of as much as 0.07% for the period 1969-1981. The model is compared with satellite observations and to other recently published models that impose immediate reradiation of blocked flux and therefore fail to predict an eleven year modulation of S.