In functional data analysis, it is often of interest to discover a general common pattern, or shape, of the function. When the subject-specific amplitude and phase variation of data are not of interest, curve registration can be used to separate the variation from the data. Shape-invariant models (SIM), one of the registration methods, aim to estimate the unknown shared-shape function. However, the use of SIM and of general registration methods assumes that all curves have the shared-shape in common and does not consider the existence of outliers, such as a curve, whose shape is inconsistent with the remainder of the data. Therefore, we propose using the *t* distribution to robustify SIMs, allowing outliers of amplitude, phase, and other errors. Our SIM can identify and classify the three types of outliers mentioned above. We use simulation and an empirical data set to evaluate the performance of our robust SIM.