Anticoagulants are the treatment of choice for pulmonary embolism. When these fail or are contraindicated, vena cava filters are effective devices for preventing clots from the legs from migrating to the lung. Many uncertainties exist when a filter is inserted, especially during physiological activity such as normal breathing and the Valsalva manoeuvre. These activities are often connected with filter migration and vena cava damage due to the various related vein geometrical configurations. In this work we analysed the response of the vena cava during normal breathing and Valsalva manoeuvre, for a healthy vena cava and after insertion of a commercial Günther-Tulip filter. Computational fluid dynamics (CFD) and patient specific data are used for analysing blood flow inside the vena cava during these manoeuvres. While during normal breathing the vena cava flow can be considered almost stationary with a very low pressure gradient, during Valsalva the extravascular pressure compresses the vena cava resulting in a drastic reduction of the vein section, a global flow decrease through the cava but increasing the velocity magnitude. This change in section is altered by the presence of the filter which forces the section of the vena cava before the renal veins to keep open. The effect of the presence of the filter is investigated during these manoeuvres showing changes in wall shear stress and velocity patterns.