Supervised multi-class target recognition algorithms label an input pattern according to the most similar training class. Typically, the number of training classes is fixed and known a priori. In practice, however, a classifier may encounter novel targets that were not seen in training and label them incorrectly. Recent work in open set recognition (OSR) develops classifiers that can identify training targets as well as previously unknown targets. This results in a reduced number of forced misclassifications by "ejecting" targets that were not present in training. Several OSR algorithms are based on support vector machines (SVMs), namely, the 1-vs-set machine, W-SVM, and POS-SVM. The 1-vs-set machine, a linear classifier, forms a "lab" around each training class to discriminate it from the remaining training classes and limit the risk of labeling open space as target space. The W-SVM uses a novel dual-calibration technique to map the SVM outputs to posterior probabilities, which are then subjected to a pair of user-specified thresholds. The POS-SVM relies on a single calibration step, but features data-driven posterior probability thresholds that are chosen automatically. Both the W-SVM and POS-SVM have the capability to use nonlinear SVM kernel functions and perform particularly well with the popular Gaussian RBF kernel. Past works have shown that these algorithms can be effective for classifying ladar and IR images with a rejection option. In this paper, we apply these algorithms to the MSTAR SAR dataset and analyze their performance for classifying known targets and rejecting unknown targets in the presence of clutter.