This research article published by the Journal of Mathematics and Informatics, Vol. 20, 2021This paper deals with the formulation and the identifiability of the variablevolume deterministic model for the endothermic continuously stirred tank reactor (CSTR). The identifiability of physical parameters of the formulated model is done by using the least squares and the delayed rejection adaptive algorithm version of the Markov chain Monte Carlo (MCMC) method. The least square estimates are used as prior information for the MCMC method. To measure the model output associated with the perturbed model parameters, we use global sensitivity analysis implemented in Latin Hypercube Sampling method. The obtained results from partial rank correlation coefficients show that six parameters are very sensitive and correlated with the model outputs. Finally, we show that the least square and the MCMC numerical results impart the model to be realistic, reliable and worthwhile to describe the dynamics of CSTR processes as physical parameters of the model are well identified and their uncertainties in the model response are analysed and quantified.