Electronic components can be affected by the dose rate from gamma rays delivered during the first few shakes (10−8 sec/shake) of an exploding nuclear device. Determining such dose rates generally requires expensive time-dependent calculations. This paper demonstrates that relatively inexpensive steady-state transport calculations can be used to bracket time-dependent peak dose rates with meaningful upper and lower limits. The model configuration consisted of a sphere of air surrounded by a spherical annulus of concrete with an isotropic source of gamma rays from fissioning 235U located at the geometric center. Steady-state calculations were made with the discrete ordinates code ANISN and the time-dependent calculations with time-dependent ANISN (TDA). The upper limit dose rates were obtained by dividing the steady-state total dose by the pulse width of the device. This is equivalent to assuming that the uncollided and air-scattered fluxes arrive at the shield simultaneously. For a lower limit calculation, only the uncollided flux was considered incident on the shield. Calculations were made for a 120-cm-thick concrete shield for ranges of 500, 1000, and 5000 m and for step-function burst pulse widths of 1 through 8 shakes. The results from the steady-state calculations generally bracketed the peak time-dependent dose rates within an acceptably narrow band except for the 500-m range at the back end of the shield where the peak time-dependent dose rates were highest for all pulse widths. This apparent anomaly is explained on the basis of using a moving boundary condition in the time-dependent solution and the effect is shown to be of no consequence.