We consider a crack partially filled with a fluid. We show that the presence of a lag avoids the appearance of pressure and velocity singularities. For the static equilibrium, we recall the previous result on the Capillary Stress Intensity Factor which provides a purely mechanical explanation of the Rehbinder effect, according to which the toughness of the material can be lowered by humidity. For the steady state propagation of a crack due to viscous fluid flow, we set the coupled system of non-linear equations.