In this work, we provide an in-depth characterization study of the performance overhead for running Transformer models with secure multi-party computation (MPC). MPC is a cryptographic framework for protecting both the model and input data privacy in the presence of untrusted compute nodes. Our characterization study shows that Transformers introduce several performance challenges for MPC-based private machine learning inference. First, Transformers rely extensively on “softmax” functions. While softmax functions are relatively cheap in a non-private execution, softmax dominates the MPC inference runtime, consuming up to 50\% of the total inference runtime. Further investigation shows that computing the maximum, needed for providing numerical stability to softmax, is a key culprit for the increase in latency. Second, MPC relies on approximating non-linear functions that are part of the softmax computations, and the narrow dynamic ranges make optimizing softmax while maintaining accuracy quite difficult. Finally, unlike CNNs, Transformer-based NLP models use large embedding tables to convert input words into embedding vectors. Accesses to these embedding tables can disclose inputs; hence, additional obfuscation for embedding access patterns is required for guaranteeing the input privacy. One approach to hide address accesses is to convert an embedding table lookup into a matrix multiplication. However, this naive approach increases MPC inference runtime significantly. We then apply tensor-train (TT) decomposition, a lossy compression technique for representing embedding tables, and evaluate its performance on embedding lookups. We show the trade-off between performance improvements and the corresponding impact on model accuracy using detailed experiments.