The lung is extremely sensitive to interstitial fluid balance, yet the role of pulmonary lymphatics in lung fluid homeostasis and its interaction with cardiovascular pressures is poorly understood. In health, there is a fine balance between fluid extravasated from the pulmonary capillaries into the interstitium and the return of fluid to the circulation via the lymphatic vessels. This balance is maintained by an extremely interdependent system governed by pressures in the fluids (air and blood) and tissue (interstitium), lung motion during breathing, and the permeability of the tissues. Chronic elevation in left atrial pressure (LAP) due to left heart disease increases the capillary blood pressure. The consequent fluid accumulation in the delicate lung tissue increases its weight, decreases its compliance, and impairs gas exchange. This interdependent system is difficult, if not impossible, to study experimentally. Computational modelling provides a unique perspective to analyse fluid movement in the cardiopulmonary vasculature in health and disease. We have developed an initial in silico model of pulmonary lymphatic function using an anatomically structured model to represent ventilation and perfusion and underlying biophysical laws governing fluid transfer at the interstitium. This novel model was tested against increased LAP and non-cardiogenic effects (increased permeability). The model returned physiologically reasonable values for all applications, predicting pulmonary oedema when LAP reached 25 mmHg and with increased permeability.