The rise time of a sonic boom shock in air depends strongly on the relaxation processes of nitrogen and oxygen. Stratification of the atmosphere leads to significant variation of the relaxation processes with altitude. J. Kang [Ph.D. thesis, Penn State (1991)] argues that the shock profile can adjust quickly enough to changes in attenuation that it always appears to be in steady state. If correct, then rise time at the ground can be calculated from local conditions only. A time domain computer algorithm, based on work by Lee and Hamilton (‘‘Time domain modeling of pulsed finite-amplitude sound beams,’’ submitted to J. Acoust. Soc. Am. in March 1994), is presented for a Burgers-type equation. The algorithm includes the effects of nonlinear distortion, thermoviscous absorption, molecular relaxation, and ray tube spreading. A parametric study of the effect of change in relative humidity shows that the steady-state assumption is not justified for sonic boom shocks in the atmosphere. A sonic boom propagated through a real atmosphere is shown to have a rise time that, in all cases run so far, is shorter than that of a steady-state shock calculated using atmospheric properties at the ground only. [Work supported by NASA.]