The working process in a double-acting piston pump in which the valves have been replaced by fl uidic diodes is investigated. A computational model of the process, constructed on the basis of a representation of a complex stream by a sum of two simple streams, the fi rst caused by the harmonic movement of the piston and the second due to the head difference between the dampers, is proposed. Analytic expressions of the fl ow-head characteristics and the pump effi ciency are obtained. It is shown that, unlike a piston pump with valve distribution, the fl ow-head characteristic of a pump with fl uidic diodes is descending and fl attened. In the region of low heads, its delivery may exceed the delivery of a pump with valves. There is an interval of heads on the characteristic in which the effi ciency of the pump is maximal. Keywords: piston pump, valves, fl uidic diode, computational model, dimensionless parameters, fl ow-head characteristic.The use of piston pumps with valve distribution [1] in the chemical, medical, and food industries represents a diffi cult process in view of the undesirable effect of the tools of these hydraulic machines (for example, valves) on liquid. In addition, as a consequence of the comparatively low degree of reliability of valves and the slowness of the parts of a valve mechanism, piston pumps are generally slow-running and of high metal content [2].Theoretical and experimental studies of valveless piston pumps [3] have investigated the force pump, or T-junction, in the central diffuser of which a piston that has been set in motion by a crank-gear mechanism and by an inlet and an outlet damper, travels. A dependence of the pump head on the frequency of the to-and-fro motion of the piston and a number of geometric parameters has been proved by numerical and experimental investigations.A micro-pump the discharge element of which comprises a membrane with piezoelectric drive has been investigated [4] with diffusor-confusor possessing diodicity provided for the purpose of implementing the distribution function [5][6][7][8][9][10]].An analytic model of the working process in a pump with vortical fl uidic diodes is presented in [11]. The tool in this pump was not a piston or membrane (as in [3,4]), but instead a gas which is alternately supplied to the pump cylinder and discharged from it. A description of such a pump is presented in the manual [12]. The device is characterized by the authors as a highly reliable pump of the type used predominantly in the nuclear industry.Thus, valveless piston pumps are effi cient and, if fl uidic diodes are used, the indicators of such pumps improve noticeably. The objective of the present study is to determine the basic parameters and characteristics of a valveless hydraulic machine (Fig.1).The block of cylinders comprises a block of one, two, or more single-acting or double-acting pistons. The calculation of the characteristics of a valveless pump is performed here for the case of a single-cylinder, double-acting pump (Fig. 2).