Infant and child mortality rates are one of the health indicators in a given community or country. It is the fourth millennium development goal that by 2015, all the united nations member countries are expected to have reduced their infant and child mortality rates by two-thirds. Uganda is one of those countries in sub-Saharan Africa with high infant and child mortality rates and therefore has the need to ?nd out the factors strongly associated to these high rates in order to provide alternative or maintain the existing interventions. The Uganda Demographic Health Survey (UDHS) funded by USAID, UNFPA, UNICEF, Irish Aid and the United kingdom government provides a data set which is rich in information. This information has attracted many researchers and some of it can be used to help Uganda monitor her infant and child mortality rates to achieve the fourth millennium goal. Survival analysis techniques and frailty modelling is a well developed statistical tool in analysing time to event data. These methods were adopted in this thesis to examine factors a?ecting under-?ve child mortality in Uganda using the UDHS data for 2011 using R and STATA software. Results obtained by ?tting the Cox-proportional hazard model and frailty models and drawing inference using both the Frequentists and Bayesian approach showed that, Demographic factors (sex of the household head) and Biological determinants (sex of the child and number of births in the past one year) are strongly associated with high under-?ve child mortality rates. Heterogeneity or unobserved covariates were found to be signi?cant at household but insigni?cant at community level.