Summary. Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently, the advent of atomic force microscopy, which operates on the same fundamental principle, has in turn revolutionized the nanoscale analysis of soft biomaterials such as cells and tissues. The paper addresses the inferential problems that are associated with material indentation and atomic force microscopy, through a framework for the change-point analysis of pre-contact and post-contact data that is applicable to experiments across a variety of physical scales. A hierarchical Bayesian model is proposed to account for experimentally observed change-point smoothness constraints and measurement error variability, with efficient Monte Carlo methods developed and employed to realize inference via posterior sampling for parameters such as Young's modulus, which is a key quantifier of material stiffness. These results are the first to provide the materials science community with rigorous inference procedures and quantification of uncertainty, via optimized and fully automated high throughput algorithms, implemented as the publicly available software package BayesCP. To demonstrate the consistent accuracy and wide applicability of this approach, results are shown for a variety of data sets from both macromaterials and micromaterials experiments—including silicone, neurons and red blood cells—conducted by the authors and others.