Two-dimensional constant-pressure filtration operations on cylindrical surfaces are investigated by using socalled power-law non-Newtonian fluids. On the basis of compression-permeability cell measurements, methods are represented for evaluating the filtration characteristics of non-Newtonian fluids by taking into consideration the internal flow-rate variation due to cake compressibility. To confirm the validity of the theory, filtration experiments are conducted with filter media of various radii by use of Hyflo Super-Cel suspended in 0.45 wt% sodium polyacrylate solutions with low N-values of about 0.3, and both filtrate volume with time and hydraulic pressure distributions within the cake are measured. It is shown that not only overall filtration characteristics but also internal cake structures can be well evaluated by the theory presented in this paper. It is also shown that filtrate volume variation can be easily evaluated by using the experimental results of the conventional uni-dimensional constant-pressure filtration on the basis of the so-called effective filtration area factor for incompressible cake.