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Interval censored failure time data occur in many areas including medicine, economics, zoology, psychology, sociology and engineering. In such studies, the variable of interest is often not exactly observed, but known to fall within some interval. In this thesis, the likelihood functions for fixed and random interval censored data are obtained. Modified Maximum Likelihood and Copula Methods are utilized for the estimation of unknown parameters. Bivariate interval censored data are also considered as a generalization in this work. To estimate the association between two random variables, we focus on the situation where they follow a copula model. To check the accuracy and efficiency of the methods, some numerical studies are conducted.Ph.D. - Doctoral Progra