The process of water reabsorption from the peritoneal cavity into the surrounding tissue substantially decreases the net ultrafiltration in patients on peritoneal dialysis. The goal of this study was to propose a mathematical model based on data from clinical studies and animal experiments to describe the changes in absorption rate, interstitial hydrostatic pressure, and tissue hydration caused by increased intraperitoneal pressure after the initiation of peritoneal dialysis. The model describes water transport through a deformable, porous tissue after infusion of isotonic solution into the peritoneal cavity. Blood capillary and lymphatic vessels are assumed to be uniformly distributed within the tissue. Starling's law is applied for a description of fluid transport through the capillary wall, and the transport within the interstitium is modeled by Darcy's law. Transport parameters such as interstitial fluid volume ratio, tissue hydraulic conductance, and lymphatic absorption in the tissue are dependent on local interstitial pressure. Numerical simulations show the strong dependence of fluid absorption and tissue hydration on the values of intraperitoneal pressure. Our results predict that in the steady state only approximately 20-40% of the fluid that flows into the tissue from the peritoneal cavity is absorbed by the lymphatics situated in the tissue, whereas the larger (60-80%) part of the fluid is absorbed by the blood capillaries.