A membrane separation apparatus comprising: a cylindrical case provided with an outlet for a membrane permeated fluid; a plurality of tubular or capillary membranes which are inserted into the cylindrical case in a substantially parallel state with each other and in a closely bundled state, the membranes each other and also the bundled membranes and the cylindrical case being bonded and fixed with a casting resin at both end portions thereof; a cap having a nozzle for a feed inlet and a nozzle for a membrane permeated fluid outlet, provided at one end of the cylindrical case; and a cap having a nozzle for a concentrated fluid provided at another end of the cylindrical case, wherein at least one open end of the tubular or capillary membranes is arranged with a slope with respect to the axis of the cylindrical case, and the nozzle for the feed inlet and the nozzle for the membrane permeated fluid are provided on the substantially same axis.