Ultrasound elastography is used to estimate the mechanical properties of the tissue by monitoring its response to an internal or external force. Different levels of deformation are obtained from different tissue types depending on their mechanical properties, where stiffer tissues deform less. Given two radio frequency (RF) frames collected before and after some deformation, we estimate displacement and strain images by comparing the RF frames. The quality of the strain image is dependent on the type of motion that occurs during deformation. In-plane axial motion results in high-quality strain images, whereas out-of-plane motion results in low-quality strain images. In this paper, we introduce a new method using a convolutional neural network (CNN) to determine the suitability of a pair of RF frames for elastography in only 5.4 ms. Our method could also be used to automatically choose the best pair of RF frames, yielding a high-quality strain image. The CNN was trained on 3,818 pairs of RF frames, while testing was done on 986 new unseen pairs, achieving an accuracy of more than 91%. The RF frames were collected from both phantom and in vivo data.