{Problems} For providing a Cu-Al-Mn-based alloy material which has excellent resistance to repeated deformations, for providing a method of producing the same, and for providing a rod material or a sheet material using the alloy material. {Means to solve} A Cu-Al-Mn-based alloy material (1) having a composition containing 3.0 to 10.0 mass% of Al, 5.0 to 20.0 mass% of Mn, and a given total content of at least one selected from the group consisting of Ni, Co, Fe, Ti, V, Cr, Si, Nb, Mo, W, Sn, Mg, P, Be, Sb, Cd, As, Zr, Zn, B, C, Ag, and misch metal, each of which is contained in a given content; with the balance being Cu and unavoidable impurities, wherein the alloy material is an alloy material having a shape that is elongated in the working direction (RD), which is the rolling direction or the wire-drawing direction, wherein in regard to a grain X (2) for which the grain length a x in the working direction of the alloy material is R/2 or less with respect to the width or diameter (R) of the alloy material,
