A separation membrane module comprising: a cylinder-shaped housing; and a number of tubular separation membranes disposed in the housing, wherein the separation membrane module is configured such that: a processing target fluid flows through the housing from its one end side to the other end side and a fluid which has permeated the tubular separation membrane flows through the tubular separation membrane and is taken out; wherein the tubular separation membrane comprises a tubular porous support body and a zeolite membrane as an inorganic separation membrane formed on the outer circumferential surface of the tubular porous support body, an end pipe is connected to one end portion of the tubular separation membrane; the end pipe is supported by a support plate which is disposed so as to traverse the housing; an end plug is connected to the other end portion of the tubular separation membrane; wherein the separation membrane module further comprises a coming-out preventive member which prevents the end plug coming out of the tubular separation membrane, wherein the module comprises, as the coming-out preventive member, a pressing plate which is opposed to the end plug and a spring which presses the end plug toward the tubular separation membrane, wherein the end plug has a rod which projects from a top end surface of the end plug and wherein the pressing plate is opposed to the end plug the pressing plate has an opening, and the rod is inserted into the opening of the pressing plate and a gap is formed between the rod and the inner circumferential surface of the opening a cylinder-shaped housing; and a number of tubular separation membranes disposed in the housing, wherein the separation membrane module is configured such that: a processing target fluid flows through the housing from its one end side to the other end side and a fluid which has permeated the tubular separation membrane flows through the tubular separation membrane and is taken out; wherein the tubular separation membrane comprises a tubular porous support body and a zeolite membrane as an inorganic separation membrane formed on the outer circumferential surface of the tubular porous support body, an end pipe is connected to one end portion of the tubular separation membrane; the end pipe is supported by a support plate which is disposed so as to traverse the housing; an end plug is connected to the other end portion of the tubular separation membrane; wherein the separation membrane module further comprises a coming-out preventive member which prevents the end plug coming out of the tubular separation membrane, wherein the module comprises, as the coming-out preventive member, a pressing plate which is opposed to the end plug and a spring which presses the end plug toward the tubular separation membrane, wherein the end plug has a rod which projects from a top end surface of the end plug and wherein the pressing plate is opposed to the end plug the pressing plate has an opening, and the rod is inserted into the opening of the pressing plate and a gap is formed between the rod and the inner circumferential surface of the opening a processing target fluid flows through the housing from its one end side to the other end side and a fluid which has permeated the tubular separation membrane flows through the tubular separation membrane and is taken out; wherein the tubular separation membrane comprises a tubular porous support body and a zeolite membrane as an inorganic separation membrane formed on the outer circumferential surface of the tubular porous support body, an end pipe is connected to one end portion of the tubular separation membrane; the end pipe is supported by a support plate which is disposed so as to traverse the housing; an end plug is connected to the other end portion of the tubular separation membrane; wherein the separation membrane module further comprises a coming-out preventive member which prevents the end plug coming out of the tubular separation membrane, wherein the module comprises, as the coming-out preventive member, a pressing plate which is opposed to the end plug and a spring which presses the end plug toward the tubular separation membrane, wherein the end plug has a rod which projects from a top end surface of the end plug and wherein the pressing plate is opposed to the end plug the pressing plate has an opening, and the rod is inserted into the opening of the pressing plate and a gap is formed between the rod and the inner circumferential surface of the opening