This study deals with the analysis of the cure rate estimation based on the Bounded Cumulative Hazard (BCH) model using interval censored data, given that the exact distribution of the data set is unknown. Thus, the non-parametric estimation methods are employed by means of the EM algorithm. The Turnbull and Kaplan Meier estimators were proposed to estimate the survival function, even though the Kaplan Meier estimator faces some restrictions in term of interval survival data. A comparison of the cure rate estimation based on the two estimators was done through a simulation study.