Several aspects of renal dysfunction was analysed biomathematically and the following results were obtained : (1) A mathematical analysis of diuretic response was developed to show a new diagnostic method for differentiating the causative factors involving in edema formation. The diuretic response test may be beneficial in dertermining the indication of antialdosterone agents in the treatment of the patients with edema. (2) A quantitative index of potassium excreting potency of the diuretic was introduced. (3) The mechanism of the delayed excretion of cations in the aged after administration of sodium thiosulfate was discussed. (4) Mathematical studies of the PSP excretion test revealed that the mode of excretion of PSP followed an exponential function. (5) The ideal excretion curves of PSP with urinary dead space is given and cases showing an abnormal curve were illustrated. (6) The mechanism of the discrepancy of PSP test and PAH clearance in the patients with heart failure was discussed. (7) Mathematical analysis of the mechanism of urea excretion in patients with renal failure revealed that there may be certain kinds of metabolic regulation and a decrease of the rate of urea production (the rate of protein metabolism) when renal function decreases.