The penetration factor for spontaneous fission has been calculated from the liquid-drop model. The transformation of the Gamow integral over the nucleon coordinates into an integral over the deformation parameters ${a}_{n}$ has been carried out hydrodynamically, assuming irrotational motion. The transformation requires evaluation of the kinetic energy in terms of ${a}_{n}$ and ${\stackrel{\ifmmode \dot{}\else \.{}\fi{}}{a}}_{n}$. Series expansions are used for the kinetic energy and for the potential energy of deformation. We have neglected all parameters but ${a}_{2}$ and carried the hydrodynamic calculations through terms in ${{a}_{2}}^{4}$. While the potential barrier is subject to several uncertainties, it has nevertheless been possible to estimate the spontaneous fission hindrance factor for the highest $Z$ elements. We find for $Z=100$ and $\frac{{Z}^{2}}{A}\ensuremath{\approx}39$ that a 1-Mev increase in barrier height should correspond to a ${10}^{3.7}$-fold increase in the half-life. This result agrees closely with the empirical hindrance factor formula deduced by Swiatecki from a correlation of fluctuations in half-lives with deviations of ground-state masses from the semiempirical mass formula. We have included some details of both the hydrodynamic and the electrostatic calculations.