In this paper, we will rely on a probability distribution, which is the exponential distribution, to build a parametric survival regression model, which is the exponential survival regression model, relying on the Cox regression model to be used in forming this model. The data used in this research were obtained through the Cancer Council in Iraq, which is affiliated with the Ministry of Health. The data was represented by a figure of patients with stomach cancer for a period of two years (2021-2022), who were registered from the onset of symptoms to hospitalization and then death or recovery., and they numbered 200 sick, the data represents the length of stay of patients in the hospital in months. This aims to study the effect of some explanatory variables on the length of survival of stomach cancer patients. The model was used to analyze the data and estimate the parameters of this model using the Bayesian method, and using goodness-of-fit tests provided by the statistical program. The ready-made Easy Fit 5.6 test is the Kolmokrov-Smirnov test, the Anderson-Darlink test, and the Chi-Squared test. It turns out that the exponential survival regression model is the most appropriate model for the data of this research, use a program (R 4.3.1), one of the most important conclusions reached was the great convergence between the exponential survival regression model for the estimated values Use a Bayesian method and the exponential survival regression model for the original values. This indicates the effectiveness of the Bayesian method in estimating parameters and its ability to approach the real data. Accurately based on the available data, and when the estimated values ​​of the model are close to the true values ​​of the model, this means that the Bayesian method that was used for estimation is highly accurate and that the model that was used for estimation has estimated it well and reflects the facts accurately.