The most important design parameters for roller presses can be referred to flow and compression characteristics of bulk materials. Usually the flow properties are measured in the low stress range 1-50 kPa at the shear rate of about 1mm/min. But this does not fit the stress regimes in the roller press. Therefore, the compression and flow behavior of the powder have to be investigated at higher pressures, shear rates, and shear displacements. These properties of bulk materials in the so-called medium pressure range 50-1000 kPa can be analyzed using a press shear cell. Tests were implemented with limestone, bentonite, and microcrystalline cellulose at average 23 degrees C powder bed temperature using shear rates from 0.00042 to 0.042m/s and a more realistic preshear displacement from 0.1 to 2m for practical applications in powder compaction. Physical observation based compression functions were developed for the low and medium pressure range, which include simple equations for the compression rate and specific compression work.