An apparatus and method for milking an animal, in particular a cow, that uses a stress measuring device for determining the animal's degree of stress and to supply stress measurement data to a memory that stores the stress measurement data. Stress measurement data are obtained before, during and preferably after milking. The stress measuring device comprises at least one instrument selected from a group consisting of an infrared meter for measuring the animal's infrared image, a hygrometer for determining the humidity of the animal's fur or nose, and iris scanner for determining the animal's eye characteristics, and an odor meter for determining the animal's breath or body odor, a muscular tension measuring instrument for determining the animal's muscular tension, an excrement analyzing instrument for determining the characteristics of the animal's excrement, and a muscle vibration meter for determining the animal's muscle vibrations.