Numerical flowfield computation studies were performed to obtain qualitative understanding of the pressure regulating mechanism of the simplest pressure regulator - an almost unknown no-moving-part fluidic device capable of keeping a constant pressure difference across a load in spite of the hydraulic properties of the latter varying in a wide range. Two application examples are discussed. In one of them, the load is a box, in which the regulator sized in hundreds of millimetres maintains pressurised atmosphere. In the other case, a millimetre-sized regulator is made as an integral part of a microfluidic circuit. Due to the purely empirical way in which the regulator geometry was developed, there has been no clear idea about its functioning. The computations run to obtain an insight into the pressure-keeping effect indicate an unexpected considerable flowfield three-dimensionality (despite the nominally two-dimensional geometry) and an essential role of a recently identified (Tesar, 2009) pressure recovery mechanism. (C) 2009 Elsevier B.V. All rights reserved.