The equations of fluid mechanics are applied to the problem of small perturbations upon a finite initial strain‐rate of a viscous fluid. The magnitude of the viscosity is such that inertia forces are negligible. General solutions are developed for the time history of buckling of a fluid with an arbitrary number of layers of different viscosities under finite compressive deformation. The effect of gravity is taken into account. Numerical solutions are derived for the single layer. Results are compared with values obtained from the theory of elasticity and viscoelasticity. The interest of the theory lies in its application to problems of folding of geological structures.