We investigate experimentally and numerically the filling of a collapsible tube, motivated by venous hemodynamics in the lower limbs. The experiments are performed by filling an initially collapsed flexible tube, applying pressure through a hydraulic circuit. The tube law and the tube tension have been previously measured. The tube shape, the flow rate and the pressure at the two ends of the tube are measured continuously. The filling occurs in three stages: a rapid equilibration of the pressure near the tube entry with atmospheric pressure, a quasi-steady filling of the tube with a linearly rising pressure, and a final stage of tube inflation. Our numerical model is the classical one-dimensional collapsible tube equations. Excellent quantitative agreement is found between computations and experimental data. We show experimentally observed shapes near the tube end that indicate possible three-dimensional effects; however these effects do not impair significantly the ability of the one-dimensional model to describe the experiment. Travelling waves of large amplitude are observed in the simulations and the experiments.