One of the main indices of maturity in avocado fruit is its firmness; this changes during the ripening and softening process starting on tree during harvesting, handling and storage. The temperature and time of storage fundamentally influence the firmness of the stored fruit and affects its shelf life later on. Monitoring the softening of fruit during cold storage might enables us to influence its shelf life. The objective of the present work was to study the effects of storage time and temperature on the softening process of avocado fruit, by means of nondestructive ultrasonic measurements. The attenuation of the ultrasonic waves, transmitted through the fruit tissue changes as a result of the progress of the fruit during storage. Several batches of avocado fruits, each stored at a different temperature, were examined until their designated storage time was completed. The fruits were subjected to nondestructive ultrasonic tests as well as to destructive penetration measurements of the tissue firmness. Statistical analysis showed quite good correlation between the firmness and the ultrasonic attenuation. This suggests that the ultrasonic method can be used as a nondestructive means of firmness measurement during low-temperature storage.