Machine learning and deep learning models are potential vectors for various attack scenarios. For example, previous research has shown that malware can be hidden in deep learning models. Hiding information in a learning model can be viewed as a form of steganography. In this research, we consider the general question of the steganographic capacity of learning models. Specifically, for a wide range of models, we determine the number of low-order bits of the trained parameters that can be overwritten, without adversely affecting model performance. For each model considered, we graph the accuracy as a function of the number of low-order bits that have been overwritten, and for selected models, we also analyze the steganographic capacity of individual layers. The models that we test include classic machine learning techniques, popular general deep learning models, pre-trained transfer learning-based models, and others. In all cases, we find that a majority of the bits of each trained parameter can be overwritten before the accuracy degrades. Of the models tested, the steganographic capacity ranges from 7.04 KB to 44.74 MB. We discuss the implications of our results and consider possible avenues for further research.