An arm structure for anthropomorphic robots minimizes the occurrence of a singularity state of a shoulder joint assembly while the arm of the anthropomorphic robot is normally working, for thereby allowing the arm to operate smoothly. The position and posture of first through third joints (11), (13), (15) of a shoulder joint assembly (5) and the position of an elbow joint assembly (6) with respect to the third joint (15) are established such that the elbow joint assembly (6) is located above a horizontal plane lying through the point of intersection of the axes (10), (12), (14) of the first through third joints (11), (13), (15), while the shoulder joint assembly (5) is operated into a singularity state wherein the first axis (10) of the first joint (11) and the third axis (14) of the third joint (15) are aligned with each other and the elbow joint assembly (6) is positioned laterally of a torso (1).