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; forming a support body including a plurality of first through holes and a plurality of second through holes from the porous material closing both end openings of the respective plurality of second through holes, 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, 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; forming a support body including a plurality of first through holes and a plurality of second through holes from the porous material closing both end openings of the respective plurality of second through holes, 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, 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.