The influence of the volume deformation rate on the intensity of piston pressing-out of oil has been investigated. The results of pressing by a piston moving with different speeds are presented. Mathematical simulation is carried out for the stage of pressing-out after the termination of sample loading, when oil release occurs due to the accumulated deformations of the skeleton. It has been assumed that in mechanical pressing there remains the least residual content of oil. A dimensionless complex representing the ratio of the characteristic times of loading to the material response (the process of pressing) has been obtained. The dependence of the rate of oil pressing-out at the stage of pressure relaxation on the dimensionless complex has been determined.