A method of producing a monolithic separation membrane structure comprising: preparing a porous material including an aggregate material, wherein the aggregate material includes at least one of alumina, titania, mullite, potsherd and cordierite having an average particle diameter of 1 to 100 micrometers, determined as arithmetic mean for the maximum diameter of 30 measured particles that are measured by cross sectional micro-structure observation by use of a scanning electron microscope (SEM); forming a support body including a plurality of first through holes (TH1) and a plurality of second through holes (TH2) from the porous material closing both end openings of the respective plurality of second through holes (TH2), then firing the support body at 500 to 1500°C for 0.5 to 80 hours, the porosity of the support body being configured to 25% to 50%, wherein the average pore diameter of the support body , as determined by using a mercury press-in method, is 5 to 25 micrometers; and forming a separation membrane used in a pervaporation method or a vapor permeation method in a tubular shape on an inner side of the plurality of first through holes (TH1), wherein the helium gas permeation resistance in the support body is less than 8.3 × 10 7 Pa·sec/m 2 , wherein the helium gas permeation resistance is measured by test method for permeability of refractory bricks according to JIS R 2115:1995, wherein the helium gas permeation resistance in the support body is adjusted to less than 8.3 × 10 7 Pa·sec/m 2 by adding a coarse-grained aggregate material to the aggregate material in the step for preparing a porous material, wherein the coarse-grained aggregate material is coarse-grained alumina having an average particle diameter, as measured by use of a laser diffraction method, of 5 to 500 micrometers that is at least 3 times the average particle diameter of the principal materials used in the aggregate material, the coarse-grained aggregate material being added at 5 wt% to 40 wt% to the aggregate material. preparing a porous material including an aggregate material, wherein the aggregate material includes at least one of alumina, titania, mullite, potsherd and cordierite having an average particle diameter of 1 to 100 micrometers, determined as arithmetic mean for the maximum diameter of 30 measured particles that are measured by cross sectional micro-structure observation by use of a scanning electron microscope (SEM); forming a support body including a plurality of first through holes (TH1) and a plurality of second through holes (TH2) from the porous material closing both end openings of the respective plurality of second through holes (TH2), then firing the support body at 500 to 1500°C for 0.5 to 80 hours, the porosity of the support body being configured to 25% to 50%, wherein the average pore diameter of the support body , as determined by using a mercury press-in method, is 5 to 25 micrometers; and forming a separation membrane used in a pervaporation method or a vapor permeation method in a tubular shape on an inner side of the plurality of first through holes (TH1), wherein the helium gas permeation resistance in the support body is less than 8.3 × 10 7 Pa·sec/m 2 , wherein the helium gas permeation resistance is measured by test method for permeability of refractory bricks according to JIS R 2115:1995, wherein the helium gas permeation resistance in the support body is adjusted to less than 8.3 × 10 7 Pa·sec/m 2 by adding a coarse-grained aggregate material to the aggregate material in the step for preparing a porous material, wherein the coarse-grained aggregate material is coarse-grained alumina having an average particle diameter, as measured by use of a laser diffraction method, of 5 to 500 micrometers that is at least 3 times the average particle diameter of the principal materials used in the aggregate material, the coarse-grained aggregate material being added at 5 wt% to 40 wt% to the aggregate material. <EOS>