The study investigated the selected mechanical properties of fresh and stored large cranberries. The analyses focused on changes in the energy requirement up to the breaking point and aimed to identify the apparent elasticity index of the fruit of the investigated large cranberry fruit varieties relating to harvest time, water content, as well as storage duration and conditions. After 25 days in storage, the fruit of the investigated varieties were found with a decrease in mean acidity, from 1.56 g·100 g−1 to 1.42 g·100 g−1, and mean water content, from 89.71% to 87.95%. The findings showed a decrease in breaking energy; there was also a change in the apparent modulus of elasticity, its mean value in the fresh fruit was 0.431 ± 0.07 MPa, and after 25 days of storage it decreased to 0.271 ± 0.08 MPa. The relationships between the cranberry varieties, storage temperature, duration of storage, x, y, and z dimensions of the fruits, and their selected mechanical parameters were modeled with the use of multiple linear regression, artificial neural networks, and support vector machines. Machine learning techniques outperformed multiple linear regression.