NOVELTY - A flexible composite membrane for the selective separation of hydrogen (H2) from a mixture has a porous substrate, preferably of (non)woven fabric and porous ceramic material (I). A metal coating (II) for separating H2, applied to a porous surface of (I), has a pattern of alternating concave and convex areas.    USE - The membrane is used for selective separation of H2 from mixtures containing H2, preferably a gas mixture, a liquid mixture containing dissolved H2 or a gaseous or liquid mixture of components giving molecular or atomic hydrogen from a single component or by reaction of 2 components (all claimed). It is also used for producing highly pure H2 containing not more than 50 ppm, preferably not more than 10 ppm impurities; and in a membrane reactor, H2 detector, H2 purification plant, electrolysis cell or hydrogenation or dehydrogenation apparatus (all claimed).    ADVANTAGE - Existing membranes comprise a pure metal film or tube, which is relatively thick or a thin coating on a porous metal membrane, both of which are too thick for high H2 permeability; or a very thin film on rigid porous ceramics, which can be made with very thin (50-500 nm) separating layers but cracks when subjected to relatively small temperature changes. The present membrane has high H2 permeability and selectivity and also great stability and equalizes and/or avoids stress caused by volume change by H2 adsorption or temperature change.    DETAILED DESCRIPTION - A flexible composite membrane for the selective separation of hydrogen (H2) from a mixture has a porous substrate, preferably of (non)woven fabric and porous ceramic material (I). A metal coating (II) for separating H2, applied to a porous surface of (I), has a pattern of alternating concave and convex areas to compensate and/or prevent stress caused by the volume change by H2 adsorption or temperature change. The entire membrane has a structure with alternating concave and convex areas.    An INDEPENDENT CLAIM is also included for the production of the above membrane by:    (i) preparing a composite of a porous substrate, preferably of woven and/or non-woven fabric, and a porous ceramic material, in which the pores on the surface have a pattern of alternating concave and convex areas; and    (ii) applying a metal coating to the surface by chemical vapor deposition, physical vapor deposition, especially sputtering and plasma coating, electroplating or electroless plating.