A method of pumping a liquid using at least one operating tank (2), a pneumatic positive pressure displacement pump (1), which is based on the fact that during pumping, inflow valve (4) closure is controlled through the introduction of a control gas into the operating tank (2) positive pressure displacement pump (1) at a pressure lower than the pressure of the compressed actuating gas and from the hydrostatic pressure at the egress of the outflow valve but higher than the hydrostatic pressure on the ingress into the inflow valve (4), which causes the inflow valve (4) to close. A device for pumping liquids comprising at least one operating tank (2) of a positive pressure displacement pump (1), to which leads a control gas conduit (10) with a control valve (11) mounted thereon, which is used to close off the inflow valve (4), and the lower section of the operating tank (2) has a narrow section in the form of a vertical cylinder (16).