In computer-aided analysis of cardiac MRI data, segmentations of the left ventricle (LV) and myocardium are performed to quantify LV ejection fraction and LV mass, and they are performed after the identification of a short axis slice coverage, where automatic classification of the slice range of interest is preferable. Standard cardiac image post-processing guidelines indicate the importance of the correct identification of a short axis slice range for accurate quantification. We investigated the feasibility of applying transfer learning of deep convolutional neural networks (CNNs) as a means to automatically classify the short axis slice range, as transfer learning is well suited to medical image data where labeled data is scarce and expensive to obtain. The short axis slice images were classified into out-of-apical, apical-to-basal, and out-of-basal, on the basis of short axis slice location in the LV. We developed a custom user interface to conveniently label image slices into one of the three categories for the generation of training data and evaluated the performance of transfer learning in nine popular deep CNNs. Evaluation with unseen test data indicated that among the CNNs the fine-tuned VGG16 produced the highest values in all evaluation categories considered and appeared to be the most appropriate choice for the cardiac slice range classification.