  We consider a porous medium being saturated with a pore fluid (Biot's
theory). The fluid is assumed as incompressible. It is shown that the general
integral of the elastic and pressure equations can be written in form of a time
dependent vectorpotential ${\bf F}$ being a solution of a homogeneous, fourth
order differential equation. The obtained equation for ${\bf F}$ is of a more
general form than the corresponding thermo-elastic vectorpotential, being a
solution of a time dependent and inhomogeneous vector bi-Laplacian. Both
vectorpotentials do, however, agree for stationary problems in general and for
certain particular boundary conditions (irrotational deformations). An example
of an irrotational deformation is studied in detail, exhibiting known
properties of classical vector diffusion
