We address stepwise crack tip advancement and pressure fluctuations, which have been observed in the field and experimentally in fracturing saturated porous media. Both fracturing due to mechanical loading and pressure driven fracture are considered. After presenting the experimental evidence and the different explanations for the phenomena put forward and mentioning briefly what has been obtained so far by published numerical and analytical methods we propose our explanation based on Biot’s theory. A short presentation of three methods able to simulate the observed phenomena namely the Central Force Model, the Standard Galerkin Finite Element Method SGFEM and extended finite element method XFEM follows. With the Central Force Model it is evidenced that already dry geomaterials break in an intermittent fashion and that the presence of a fluid affects the behavior more or less depending on the loading and boundary conditions. Examples dealing both with hydraulic fracturing and mechanical loading are shown. The conditions needed to reproduce the observed phenomena with FE models at macroscopic level are evidenced. They appear to be the adoption of a crack tip advancement/time step algorithm which interferes the least possible with the three interacting velocities, namely the crack tip advancement velocity on one side, the seepage velocity of the fluid in the domain and from the crack (leak-off), and the fluid velocity within the crack on the other side. Further the crack tip advancement algorithm must allow for reproducing jumps observed in the experiments.