PROBLEM TO BE SOLVED: To provide a magnesium alloy sheet material which is lightweight and is capable of room temperature molding, a method for producing the same, and a press molding.SOLUTION: The magnesium alloy sheet material with excellent room temperature moldability and excellent damping performance is produced and provided, wherein a magnesium alloy sheet containing 0.05-3 mass% of an element whose solid solubility limit to magnesium at room temperature is less than 1 mass% is used as a material, and heated and annealed to 470-540°C to obtain a grain size of 20-100 μm, and after a sequence of steps, in which warm rolling at 100-250°C with the total rolling reduction of 16-30% in one pass or a plurality of passes is performed, is appropriately repeated, finish annealing is performed at 150-400°C as needed, thereby randomizing crystal orientation distribution. Thus, the magnesium alloy sheet material excellent in damping performance and applicable to a wide range of areas, such as aviation and spac
