Mathematical model of filtration on hollow fiber with compressible cake formation is derived in this article. Fluid flows in dead-end arrangement from outside to inside of the fiber due to constant rate suction at permeate side. Pressure drop caused by permeate flow in narrow fiber channel and pressure drops across the membrane and across compressible filtration cake are implemented in the model. Numerical Solution of the model equations by finite volume method is applied. Dependences of cake thickness, flux and pressure inside the fiber on fiber axial coordinate are shown. Results show that the model could be useful for prediction of initial stages of filtration on hollow fibers, especially when the cake with higher specific resistance is formed.