A mathematical model of the interactions within a milking machine teatcup has been developed, which describes the relationship between liner wall movement, pressures and flow rate when milking without an air inlet. It is based on equations of motion for a column of incompressible fluid and requires a second-order, non-linear differential equation to be solved. Incorporating a non-return valve allows hydraulic milking to be modelled, and the comparison between predicted and measured pressures, flow rates and liner wall movement when milking hydraulically is shown. The model can be used to optimize milking conditions to reduce vacuum peaks, improve liner opening and thus maximize flow rate. * Present address: 57 Oatlands Road, Reading RG2 9DN, UK.