This study, based on 1993-94 Bangladesh Demographic and Health Survey (BDHS), attempts to identify important factors influencing infant and child mortality. Application of Cox`s proportional hazard model suggest that socio-economic status of the parents are associated with child survival. The factors that have received the most attention are maternal education, sanitation and access to safe drinking water. For instance, risk of infant mortality is 13% lower among the women having primary education and 25% lower among the women having secondary or higher education than those having no education. It was observed that 35 and 29% lower among the households having safe drinking water and good sanitary facilities, respectively than those who do not have such facilities. Similarly, risk of child mortality decreases with increased female education and wider access to safe drinking water and good sanitary facilities. So attention should be given to female education and expansion of public health system in order to reduce the risk of infant and child mortality.