A pump system has at least one fluid container (2) which comprises an inlet (4) and an outlet (6), at least one pump (8) arranged in the inlet (4) or the outlet (6), and a control device (16) which includes a flow evaluation device for determining a flow through the fluid container (2) of the pump system. The flow evaluation device is configured such that the flow evaluation device uses a system model for determining the flow. The system model includes at least two different sub-models, a sub-model which describes the inflow behavior of the fluid container (2) and a sub-model which describes the outflow behavior of the fluid container (2). A corresponding pump flow evaluation method is provided.