A variational principle is used in conjunction with the finite-element method to solve the initial boundary value problem of flow in a saturated porous elastic medium. This results in a powerful solution technique for the determination of stress and displacement history, both for the solid and the liquid phases, for arbitrary boundary conditions and within complex geometrical configurations. Direct application is to problems of consolidation and drainage of saturated soils under load. Linear theory of the coupled fields is treated but extension to nonlinear problems is possible through use of incremental procedures.