Calibrating inelastic models for high temperature materials used in advanced reactor heat exchangers is a critical aspect in accurately predicting their deformation behavior under different loading conditions, and thus determining the corresponding failure times. The experimental data against which these models are calibrated often contains a wide degree of variability caused by heat-to-heat material property variations and general experimental uncertainty. Most often, model calibration is done against mean of these experimental data without considering this variability. In this work we aim to capture the bounds of the viscoplastic parameter uncertainties that enclose this observed scatter in the experimental data using Bayesian Markov Chain Monte Carlo (MCMC) methods. Bayesian inference provides a probabilistic framework that allows to coherently quantify parameter uncertainties based on some prior parameter distributions and the available data. To perform the statistical Bayesian MCMC analysis, a pre-calibrated model, fitted against mean of the experimental data, is used as an initial guess for the prior distribution and bounds, while further sampling is done using Meteropolis–Hastings algorithm for four Markov chains in tandem, to finally obtain the posterior distribution of the model parameters. Since different inelastic parameters are sensitive to different tests, data from multiple experimental conditions (tensile, and creep) are combined to capture the bounds in all the parameters. The developed statistical model reasonably captures the scatter observed in the experimental data. Quantifying uncertainty in inelastic models will improve high temperature engineering design practice and lead to safer, more effective component designs.