An elevator without counterweight may Include an elevator car suspended by a hoisting rope, a traction sheave operatively connected to the elevator car by the hoisting rope, and a brake structure configured to engage with the traction sheave in a braking operation in an upward motion and a downward motion of the elevator car. The brake structure may include first and second brake elements. The first brake element may include a surface engageable with the traction sheave, and first contact and sliding surfaces. The second brake element may include second contact and sliding surfaces. The first sliding surface may slide along the second sliding surface relative to the second brake element when the elevator car moves with the upward motion. The second contact surface may contact the first contact surface to stop a sliding motion of the first brake element when the elevator car moves with the downward motion.