Background: Reducing child mortality is now a global concern. Globally, Under-five child mortality rate was decreased by 58% in 2017. In the 2016 EDHS report, under-five mortality was declined to 60% in Ethiopia in 2016. Methods: The data for the study was obtained from EDHS data conducted in 2016. In the study, we analysed the data using stratified Cox proportional hazard model and multilevel lognormal parametric survival model. Results: From the total of 10,331 under-five children, 635 (6.1%) deaths had occurred in the 2016 EDHS data. And, the overall probability of survival value was near to 0.92 with the estimated mean survival time was 55.4 months. In the study we found that covariates like birth type of the child, family size, wealth index, frequency of listening radio, place of delivery, place of residence, and geographical region were significant factors for the death of under-five children in stratified Cox proportional hazard model. In the multilevel lognormal parametric survival model, we found that the random-intercept effects of variations between region and household levels on the mean survival times of the children were 1.7 and 0.9, respectively. These values indicated that we had enough evidence for the existence of unobserved heterogeneities between regions and households. Conclusion: The covariates like birth type of the child, family size, wealth index, frequency of listening radio, place of delivery, place of residence, and geographical region covariates were significant factors for under-five children mortality using stratified Cox proportional hazard regression model. In the random-intercept effects model, the two estimated variances of the random-intercept effects for regional and household levels were 1.7 and 0.9, respectively. The values indicate that we have enough evidence that there were unobserved heterogeneities on the mean survival times of the under-five children between regions and households levels. Further studies should be conducted to identify the individual, household, and community-level factors associated with infant and child mortality in Ethiopia.