In the method, trenches are etched and, in between, bit lines (8) are in each case arranged on doped source/drain regions (3, 4). Storage layers (5, 6, 7) are applied and gate electrodes (2) are arranged at the trench walls. After the introduction of polysilicon, which is provided for the gate electrodes (2), into the trenches, the top side is ground back in a planarizing manner until the top side of the covering layer (16) is reached, and afterward a polysilicon layer (18), which is provided for the word lines, is applied over the whole area and patterned to form the word lines.