Abstract: A filter element intended for tangential-flow filtration has an elongated support body of porous ceramic material with coaxial channels running through the support body and provided on their surface with a ceramic membrane having a calibrated pore structure. A portion of the fluid flowing through the channels penetrates the membrane and exits as filtrate at the circumferential surface of the support body. The shape of the outwardly facing channel wall is adapted to the external shape of the support body and there it has a uniformly thick wall corresponding to the mechanical stress. The shape of the channel walls is configured such that the webs remaining between the channels flare outwardly wedge-wise. The filter element thus configured has a support body with a reduced resistance to the passage of the filtrate flowing through it.