A filtering device includes: a fluid-collecting tube; a plurality of positioning trays sleeved around the fluid-collecting tube and stacked one above the other; and a plurality of membranes alternating with the positioning trays. Each of the membranes is sandwiched between an adjacent pair of the positioning trays. Each of the positioning trays includes first and second engaging members. Each adjacent pair of the positioning trays are coupled to each other and are rotatable relative to each other between a first relative position and a second relative position. The first engaging member of each of the positioning trays is engageable with the second engaging member of an adjacent one of the positioning trays.