It has become evident that the float zone crystal growth method and isothermal liquid bridges may be very sensitive to the residual acceleration environment of a spacelab. Indeed, the shape equilibria show a high degree of sensitivity and, thus, even the small steady acceleration associated with the effective low gravity environment of a spacecraft cannot be ignored. Using a slender-body approximation, the problem of determining the axisymmetric response of the shape of the free surface of a cylindrical liquid column bounded by two solid regions is modeled by a 1-D system of nonlinear equations. It is found that the sensitivity of the zone shape depends on the static Bond number, B 0, aspect ratio, and viscosity, as well as the amplitude and frequency of the disturbance. The general trend is an increase in tolerable residual gravity with increasing frequency. At the eigenfrequencies of the zone, however, there are dramatic deviations from this trend. At these frequencies the tolerable residual gravity level can be two orders of magnitude lower at this frequency. For the cases considered the values of B0 were taken to be 0.002 and 0.02 and the dimensionless viscosities, C = v(p/γR 0)1/2, used were in the range 0.001-0.01. Aspect ratios ranging from 96.3% to 82.7% of the Rayleigh limit were examined. For these cases, the frequencies associated with the lowest tolerable acceleration have been found in the 10-2-10-1 Hz range. In terms of previously recorded and predicted residual accelerations, the sensitive frequency ranges for the cases examined are 10-2-10-1 Hz and 1-10 Hz. Maximum tolerable residual gravity levels as low as 10-6 g have been calculated. The effect of viscosity is seen to increase the tolerable acceleration level for all frequencies. The equilibrium shape, as determined by the steady background acceleration, has a pronounced effect at low frequencies. A change in slenderness of the bridge markedly changes the sensitivity to residual acceleration as the Rayleigh limit is approached. © 1990 American Institute of Physics.